NEW YORK – Hudson River Trading is moving from 4 World Trade Center to new space at 3 World Trade Center, which opened last June.
Silverstein Properties Chairman Larry Silverstein announced HRT has signed a lease with Hudson River Trading (HRT) for 136,000 square feet of office space at 3 WTC.
Founded in 2002, HRT develops automated trading algorithms using advanced mathematical and statistical modeling techniques in an extremely high-performance computing environment. With offices around the world, HRT trades equities, futures, options, currencies and fixed income on over 50 markets worldwide.
HRT, which is currently located on the 57th and 58th floors of 4 World Trade Center, will move its headquarters to the 74th, 75th, 76th and 77th floors next door at 3 World Trade Center. Included in the lease is an iconic 5,000 square foot outdoor terrace that was made possible by the 76th floor setback of the Richard Rogers designed tower. HRT will now have sole access to the space, at 935 feet, the highest private outdoor terrace in New York City, along with panoramic views of New York Harbor and the Midtown skyline.
Jeremy Moss, Director of World Trade Center Leasing for Silverstein Properties, led the negotiations for the landlord, together with the CBRE agency team including Mary Ann Tighe, Ken Meyerson, Evan Haskell, David Caperna, Adam Foster, Steve Eynon, Rob Hill. Hudson River Trading was represented by Sacha Zarba and Chris Corrinet of CBRE. HRT has also hired Gensler Architects to design its space. Gensler designed the company's existing headquarters at 4 WTC, which also features an outdoor terrace.


Daniel Morad is a talented young racing driver from Toronto. He was born on April 24, 1990. After a successful karting career, he won the Formula BMW US Championship in 2007, and was placed fourth in the Formula BMW world finals in Valencia.
He has also raced in Formula Atlantic and A1GP competition.
Podcast 414 features an exclusive conversation with this talented driver.
Morad will soon announce his racing plans for the 2010 season. Meantime, we invite you to visit his website www.danielmorad.com for more information on his career.


text:
General National Socialist Subjects
NAZI REGALIA BOOK (Item GEN 1-2)
DESCRIPTION: This long-out-of-print book (1974) is very sought after today, and very high premiums have been paid for copies that have managed to be found. This book was once deemed the "hornbook" of the hobby. The book contains 157 pages with over 100 brilliant four-color photos of medals, badges, uniforms, documents, weaponry, cloth insignias, etc. We have several copies--never used. They have sat on a shelf for almost 30 years. They won't last long, so buy now. It's great for photos and information, but remember, it's an important collectible on its own.
[Click for Full Photo]
SS REGALIA BOOK (Item GEN 1-3)
DESCRIPTION: Long out of print, this was the "hornbook" for SS collectors back when it was printed in 1974. We have a small accumulation of these books that are in great condition. Besides being a fairly good reference with over 100 brilliant four-color photographs, the book itself is considered a rather rare collector's item on its own. Some of these books when found have brought $45 to $55 in some of the mail-order auctions as far back as 5 years ago. What we have on stock will not last long because some dealer will swoop up the remaining stock for sure, so now is the time to buy.
Deutschland Erwacht, Germany Awakened (Item GEN 1-5)
DESCRIPTION: This is the famous cigarette picture book tracing the history of the NSDAP (Nazi Party) from its early history to 1933, the eve of total power in Germany. This is a book by a cooperative effort of the central offices of the NSDAP and the Cigarette Picture Service in Hamburg. Many thousands of these handsome volumes were published, but specimens like this, especially in this immaculate condition, are quite scarce today. The fine glossy pictures are mostly pasted into the book and the work is complete. There are 152 pages and a spectacular foldout at the back of the review of the SA and SS standards at the Nuremberg party rally or 1933. The volume has literally hundreds of fine historical black-and-white pictures and a very moving full-page illustration in color of an SA man with Standarte who gazes at a young trooper who has died for the cause. The book measures 12 ½ x 9 ½ inches and is about an inch thick with brown, fabric-type covers. It truly is a handsome book and its historical importance cannot be minimized.
Book Deutschland Erwache (Item GEN 1-5b)
DESCRIPTION: Here is another copy of this, the hornbook of the Nazi Movement. It is the exact duplicate of the one above except the condition is not quite as good. There is a bit of cover fraying top and bottom and there are two pictures that someone tried to tape in when they came loose years ago and the tape turned dark and stained. The very edges of the picture, however, both are there (intact). The color pictures and the black and white are exemplary. The huge foldout of the SA at Luitpoldhain in 1937, is all there and in fine condition. The title on the front is a bit faded, but the inside pages are in great condition.
Page Two
Page Four
Page Five
Page Seven
Page Eight
Page Ten
Page Eleven
Page Twelve
Page Thirteen
Page Fourteen
Page Fifteen
or call at 706.782.1668 or 706.782.4398.
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redpajama_set_name: RedPajamaCommonCrawl


USS Mayrant was a Benham-class destroyer laid down on April 15, 1937 and launched on May 14, 1938. It was commissioned on September 13, the following year under Lt. Comdr. E. A. Taylor's command with the hull number DD-402 and served in the US Navy for 7 years until it was decommissioned on August 28, 1946. During its activity, the ship carried a complement of 184 people on board and had the main missions in Boston, Iceland, Halifax, South Africa, Scapa Flow, Palermo or Okinawa. For the services brought to the country during the World War II, USS Mayrant received 3 battle stars.


Posted on July 21, 2018 by Tish Farrell	This entry was posted in Botany, Environment, poetry and tagged #6WS, #SixWordSaturday, Hugh MacDairmid, spear thistle, Tish Farrell Writer, weeds. Bookmark the permalink.
Thanks, Debbie. The pirly-wirly is a treasure, isn't it.
Thistles everywhere! Have a good weekend, both.
They certainly do get everywhere. They made to Australia and have colonized many areas. Over here they are classified as a noxious weed.
They are pretty noxious out the field behind the house. The creeping thistles are the worst for making clouds of seed heads.
They do tend to spread quickly when they colonize an area.
I often wondered how they progressed!
Definitely veering towards Wee Free Men territory.
If only the birds would eat all of the seeds. Can't tell you how many we have choped down in the pastures.They are pretty even though they are bad.
Hard work chopping them down.
How lovely to have a well-behaved thistle. They are so structurally pleasing.
beautiful plant, difficult to love when you've stepped on the new leaves, barefoot; but the goldfinches feast there, come fall, so all is forgiven. My own fault, actually, I used to use thistle seed in the finch feeder, and…well…now they gather their own and I wear boots outside.
I feel as though I am following you around Tish. Yet another I photographed on Thursday. Seems these thistles stretch from one end of the British Isles to the other!
Love that last image, Tish!
Stunning photos of the monster! I think the attempt to replicate home of our early Scottish settlers has a lot to answer for. Have you read the whole poem? Do you have Scottish blood???
No, I've not read the whole poem. Much of it looks inscrutable. It mostly seems to be the state of Scotland stream of consciousness. And no. No Scots blood as far as I know, though I did live in Aberdeen for a few years where they have their own vernacular, Doric.
I thought Scots blood would be the only thing to drive you through the whole poem – reading which I wouldn't put beyond you!
Love your garden images, beautiful. The thistle thrives here in our wild garden as well, I let it be. It's a better pest than stinging nettle.
What was it about the 1920s and Celtic writers' impenetrable prose or poetry? Joyce, McDairmid. I do love reading Scots though. I think it's still the language of my inner voice. Which I suppose only demonstrates that you can take the girl out of Kirkcaldy but you can't take Kirkcaldy out of the girl.
I can still remember my Afghan hound who got loose around a thistly woods and came home with a coat that could only be shaved. It was impressive.
Oh dear oh dear. I can only imagine how very awful a tangle that dog must have been in. Thistles do go to utter extremes when it comes to procreation.
They are certainly very pretty but the only member of that family I like to see in my garden is the globe artichoke.
Yay, to globe artichokes, though this year mine have been either frozen to death, baked or infested with black fly. The one edible one though was wonderful.
🙂 Ah, yes, the spurtle. I am the proud owner of a spurtle.
Border Scots dialect, it probably gets more difficult further north then. I took similar thistle photos this weekend, but mot as good, on my phone.


text:
Michael Bolton announces huge Manchester show – how to get tickets
By Georgina Pellant
Every mum's favourite crooner Michael Bolton will return to the UK in 2020 for the Love Songs Greatest Hits tour.
He will be performing at The Bridgewater Hall in Manchester on 28th September next year, and tickets will go on sale Friday 6th December at 10am.
Known for hits such How Am I Supposed to Live Without You, How Can we Be Lovers, When A Man Loves A Woman and Time, Love And Tenderness he has sold more than 65 million albums and singles worldwide.
Michael has also won two Grammys for Best Pop Male Vocal Performance and six American Music Awards.
He's got a star on the Hollywood walk of fame and has seen nine studio albums rank in the top ten, with nine number one singles to date.
He has also written with some of the greatest and most diverse talents of our time, including Bob Dylan, Paul Stanley, Lady Gaga, Diane Warren, and David Foster.
His most recent album, Symphony Of Hits, celebrates 50 years in the entertainment industry.
The collection of greatest hits is newly recorded with a complete symphony orchestra and was recorded at All Saints College Performing Arts Centre in Perth, Australia.
Michael will be performing at the Bridgewater Hall on 28th September 2020, and tickets will go on sale Friday 6th December at 10am.


One of the most frequently produced plays in regional theater is Mark Harelik's "The Immigrant," which received its world première at the Denver Center Theatre Company in 1985. It was a real three-handkerchief play then - but also uplifting and joyful.
Now the play has been reworked into a musical, playing at the Denver Center and opening at the Coconut Grove Playhouse in Florida March 5. While some songs could be more melodic, others are beautiful enough to make an audience catch its breath.
"The Immigrant" is about the search for life's meaning as much as it is the story of generations of new Americans seeking refuge from persecution, escape from degrading poverty, and political and social freedom in the Promised Land. So often that story is told in dark terms - the disappointment of exploitation and intolerance that can greet immigrants.
Mr. Harelik originally based the play on his own family's experiences: His grandfather and grandmother were Jewish refugees who escaped persecution in Russia.
"The main thing is that the [musical] stopped being about my grandparents," says Harelik in a recent interview. "I removed most of the personal references. Now the four characters are archetypal."
It's true. The new musical is less personal, more universal, and strangely enough, more poignant. The basic story arc is the same: When Haskell arrives in Texas, he speaks little English, has no money, and hawks bananas for a penny each. (Adam Heller's performance as Haskell is a comic delight.) Ima and Milton take him in and set him up in business - Ima because she's a Christian with a heart of gold, and Milton because he has good business sense and more humanity than he cares to acknowledge.
Haskell saves enough to send for his wife, Leah (played with warmth and insight by Jacqueline Antaramian), and together their business thrives. Haskell and Leah raise three sons (offstage), one of whom is named after Milton. But when World War II breaks out, Haskell and Milton fall out over politics. Years later, before Milton (Walter Charles gets the curmudgeon right) dies, they make up. It is Haskell who apologizes, acknowledging his gratitude to the cantankerous old dear.
The most beautiful songs are actually those that illumine different aspects of love. At the end of the play, Ima (charming Cass Morgan), who is a Baptist, sings about having tried to get her husband to "Take the Comforting Hand of Jesus." The song's not about dogma; it's about the love she feels for her husband.
But the best of all the songs is "The Stars," which Haskell sings at the beginning of the play, Leah sings toward the middle, and Leah, Ima, and Haskell sing together at the end. The lines "Nothing is ever lost" and "God is there in the dark" speak to the religious belief systems of the characters, of course. But "Nothing is ever lost" also is an affirmation that life has meaning and, despite all the losses the characters experience, that meaning is permanent. Leah kissed her mother goodbye, never to see her again when she followed her husband to the new world. Ima's son left home never to return, and her husband falls ill and dies. Still, "Nothing is ever lost."
And despite the apparent darkness (from persecution to culture shock to intolerance), the stars light the way and "God is there in the dark." It's a brave lyric to write. It's not postmodern or hip. But it is something millions of people have experienced, and it reflects the spirit of the play. The melody echoes a Jewish folk song. It falls on the ear like a hymn, yet it suits the theatrical moment - strong, handsome, and bright as diamonds.
Neither the music nor the play itself is sentimental or manipulative. "All of the real value of your relationships continue," playwright Harelik says. Again, it is experience that speaks.
"The song came very fast," says lyricist Sarah Knapp, whose husband, composer Steven M. Alper, wrote the lovely music. "I remember it didn't seem slick. But I didn't mess with it. It seemed very right.... I was thinking and feeling for every one of the characters. 'Nothing is ever lost' is comfort for all of them."
But there's nothing ironic or cynical about the story or music. Isn't that gauche? "I'm aware that we are not cynical," laughs Ms. Knapp. "Maybe I'm going to catch it for this - but the song is what it had to be."


text:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
Licence curtailed after 16 prohibitions
18th December 1970, Page 34
Page 34, 18th December 1970 — Licence curtailed after 16 prohibitions
Keywords : Islay, Aga, Business / Finance
• Spiralling costs of vehicle maintenance were referred to at a public inquiry in Aberdeen last week when Kelman of Turriff was called to show cause under Section 69 of the Road Transport Act, 1968 why its licence should not be revoked, suspended or curtailed. The case arose from eight immediate and eight delayed prohibitions on vehicles imposed by vehicle examiners between May and October.
Mr James Kelman, partner in the firm, explained that its inspection and maintenance department at Turriff employed four men full time, plus casual workers at the weekend. During the past year the firm had lost over 4720 manhours because of illness and domestic trouble.
Since July the firm had established a fully equipped maintenance depot at Airdrie, Lanarkshire, employing five people. Here south-going vehicles were inspected at least once every 72 hours.
Mr F. Lefevre, for the firm, said expenditure on maintenance and repairs this year represented 17 per cent of the gross turnover of the business, against eight per cent in 1966.
The reorganization programme, since July, had cost immediate capital outlay of £61,155 and he pleaded that this represented sufficient penalty for the shortcomings Kelmans had been called upon to answer.
Mr A. B. Birnie, the Scottish LA, ruled that it would be inappropriate if the Authority were not to impose some penalty and he curtailed the licence from 28 to 20 vehicles, in effect entirely removing the firm's margin and cutting out one vehicle at present in use.
Islay Transport Services, Bowmore, with the same directors as Kelman, had an application for three vehicles turned down. The firm is engaged in the carriage of whisky from the Island of Islay to West Scotland, with return loads of grain for the distilleries.
People: A. B. Birnie, F. Lefevre, James Kelman
Locations: Aberdeen


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text:
Dawson City tourists can team up to solve a murder most foul
The door closed, followed by the click of a lock. The timer showed 60 minutes. That's how long we had to solve a murder and find our way out of the room.
PIerre Chauvin
The door closed, followed by the click of a lock. The timer showed 60 minutes.
That's how long we had to solve a murder and find our way out of the room.
Thankfully, failing to solve the murder in the allotted time would only damage our ego, because the scene isn't from a horror movie but from Parks Canada's newest attraction: the Dawson City Escape Room.
The game takes place in a room inside the Commissioner's Residence on Front Street.
It's based on the true story of the murder of Leon Bouthillette, whose decomposed body was found south of Dawson City on July 14, 1902.
The five of us quickly split tasks, some deciphering clues and others looking around the room for new ones.
Adrenaline was rushing through our veins. While we were racing against time, a man was watching our every move from a monitor one floor below using a remote camera.
In the past two years, escape rooms have flourished across the world, with as many as 15 in Vancouver alone. Last April, one opened near the Takhini Hot Springs outside Whitehorse.
Escape rooms are built around a fictional story, requiring teams to solve puzzles, riddles and other headache-inducing scenarios to find their way out in the allotted time.
The advantage of setting up an escape room in Dawson City is that Parks Canada didn't need to create a fake gruesome murder story.
"We have such a rich history of larger-than-life, you-wouldn't-believe-it-was-true-even-if-we told-you kind of stories," said Parks Canada's Teresa Conkin, who worked on the escape room.
The Parks Canada team in Dawson set out to turn the story of how a North-West Mounted Police Officer solved the gruesome 1902 murder into a one-hour puzzle.
The room inside the Commissioner's Residence was outfitted to resemble the officer's room at the time.
The residence itself is the ideal location: the renovated Victorian-era building has kept its Gold Rush vibe, making the story much more real.
For Parks Canada, the escape room is the ideal way to reach a younger audience, pairing fun with historical events.
The game creator, a consultant hired by Parks Canada, opted to rely heavily on a mix of clues and puzzles to recreate the mystery.
"He took the story and wove it into a puzzle," Conkin said. "The puzzle is all connected to the story."
While willingly locking yourself in a room with four other people for an hour to solve puzzles might not necessarily sound like fun, the creators of the game made it entertaining enough that time flies by.
The escape room has been open for a week, and so far there's been a success rate of about 10 per cent.
Two Yukon News reporters paired with three other visitors were able to solve the murder in 44 minutes, breaking the previous record of 49 minutes.
It was difficult but doable.
After all, the Mountie who solved the original case only had one clue to go on: a keychain.
"It was quite an impressive feat to solve this murder," Conkin said.
Even groups who didn't make it in time still had fun, she said.
"Whether they managed to escape within the time allotted or not they came out buzzing with excitement."
Solve the murder and you will receive a personalized North-West Mounted Police Certificate of Genius, which, mounted in the right frame, looks like a genuine credential.
Because the residence is a historic site, and to make sure everything runs smoothly, staff monitor the room with a camera and can communicate with the team via walkie-talkie.
The participants can get two clues if they're stuck.
Back when it happened, the murder triggered an international man hunt.
The detective in charge, W.H. Welsh, tracked the murderer to the United States, travelling thousands of kilometres.
"It was an incredible journey to solve that murder," Conkin said.
For the murderer, it didn't end so well: he was hanged in 1903.
The Dawson City Escape Room runs until the end of the season, Sept. 25, and will be back next summer.
Parks Canada recommends groups of four to six for the experience. Smaller groups can be paired with one another.
Entry is $22 per participant. To book, call 993-7210, email dawson.info@pc.gc.ca or visit the Dawson City Visitor Information Centre.
Contact Pierre Chauvin at
pierre.chauvin@yukon-news.com
Remembering Wayne Roberts
Clear your arteries – the burgers have arrived


text:
\section{Introduction}

New one-dimensional integrable lattice models were introduced in \cite{amp},
within the framework  of the Quantum Inverse Scattering Method
\cite{qism1,qism2,qism3}.
They correspond to a generalization whereby every state of the original
model, for the defining representation of the Lie algebra $A_{m-1}$
(see for instance \cite{jimbo}), is replaced by an arbitrary number of copies.
The structure of the $R$-matrices  is left unchanged by the
replacement, but a usual property, crossing unitarity, is lost.
It is however still possible to construct integrable open boundary conditions.
The eigenvalue set of the transfer matrix is unchanged,
while the degeneracies increase \cite{danzi}.
For integrable periodic boundary conditions the
eigenvalues and degeneracies change \cite{amp}.

These models are of interest in some one-dimensional reaction-diffusion
processes \cite{adhr}.
(Similar but different models were also considered in \cite{alcabar}
as generalizations of the t-J model.)
They also appear in connection   with the Hubbard model
for electrons, as a specific limit \cite{aars,hakobian} or,
for $m=2$ and at a certain  value of the quantum parameter, as building
blocks for the natural generalizations of the Hubbard model \cite{ff,piezi}.
Upon fermionization, the multiple-states appear as different flavors of
fermions. The general Hubbard models can then be seen as  multichannel
versions of the original model.

All the `multiplicity' $A_{m-1}$ models of \cite{amp} correspond
to the {\it defining} representations of the Lie algebras $A_{m-1}$.
As no quantum group formalism \cite{jimbo}
is yet known for the multiplicity models,
it is not clear whether generalizations to higher
dimensional representations are possible.
There is no obvious or systematic way
to do  a  replacement of states by multiple copies in higher
dimensional $R$-matrices. The fusion method, known to work for ordinary
models, turns out to give the correct answer for the multistate models.

The main result of this work is to show that such generalizations exist.
I first review the fusion method for obtaining
higher dimensional solutions of the Yang-Baxter equation starting
from an arbitrary solution. The results of section \ref{fusionsec}
are quite general and require only a minimal number of assumptions.
This  method is then shown to work for the  models at hand.
This yields  multiplicity models corresponding to some  higher
dimensional representations, and also shows that iterated fusions
are possible. Thus  all  higher dimensional representations of $sl(m)$
have  multistate generalizations.
Hamiltonians are obtained as the derivative of the new $\check{R}$-matrices.
I consider in detail  the spin-0 and spin-1 models  of $sl(2)$,
and give explicit expressions for their $R$-matrices.

\section{Fusion}\label{fusionsec}

The multiple fusion procedure for $sl(m)$  $R$-matrices was developed
in \cite{krs}. The idea for
other algebras is the same \cite{kr,kns}. A simple description was given
in \cite{mene} for  two successive fusions. Here I review
the fusion method and give some additional general results.

The models  are defined through their $R$-matrices.
These are  solutions of the Yang-Baxter equation (YBE):
\begin{equation}
R_{12}(\lambda-\mu) \, R_{13}(\lambda) \, R_{23}(\mu) =
R_{23}(\mu) \, R_{13}(\lambda) \, R_{12}(\lambda-\mu) \label{ybe}
\end{equation}
Here and below, the notation $\CO_{ij}$ ($i \not= j$)
means that the operator $\CO$ acts non-trivially on the $i^{\rm th}$
and $j^{\rm th}$ spaces, and as the identity on the other spaces:
$\CO_{ij}=\sum_k {\Bbb I}\otimes \cdots \otimes a_k^{(i)}\otimes \cdots \otimes
b_k^{(j)}\otimes \cdots \otimes {\Bbb I}$ (if $i<j$),
where $\CO =\sum_k a_k \otimes b_k$.
Note also that the three spaces 1, 2 and 3 need {\it not} be copies
of the same space.

Consider {\it any} solution $R$ of the Yang-Baxter equation (\ref{ybe}),
which becomes proportional to  a projector at some special value $\rho$ of
the spectral parameter. Define the projector $\pi^{(1)}$ so
that $\pi^{(1)}\propto R(\rho)$, and let
$\pi^{(2)}={\Bbb I}-\pi^{(1)}$
be the orthogonal complementary projector.
Setting $\lambda-\mu = \rho$ in the YBE one obtains:
\begin{equation}
\pi^{(1)}_{12}\,  R_{13}(\lambda)\, R_{23}(\lambda-\rho) =
R_{23}(\lambda-\rho)\, R_{13}(\lambda) \, \pi^{(1)}_{12} \label{ybep}
\end{equation}
Left and right multiplication of
(\ref{ybep}) by $\pi^{(2)}_{12}$ yields two equations
\begin{eqnarray}
& & \pi^{(1)}_{12} \, R_{13}(\lambda)\,  R_{23}(\lambda-\rho)\,
\pi^{(2)}_{12} =0 \label{ybep1} \\
& & \pi^{(2)}_{12}\,  R_{23}(\lambda-\rho)\,  R_{13}(\lambda) \,
\pi^{(1)}_{12}= 0 \label{ybep2}
\end{eqnarray}
Define two  fused matrices  by
\begin{eqnarray}
R^{(1)}_{<12>3}(\lambda) &=&
\pi^{(1)}_{12}\, R_{13}(\lambda)\, R_{23}(\lambda-\rho) \,\pi^{(1)}_{12}\label{fus1}\\
R^{(2)}_{<12>3}(\lambda) &=&
\pi^{(2)}_{12}\, R_{13}(\lambda)\, R_{23}(\lambda-\rho) \,\pi^{(2)}_{12}\label{fus2}
\end{eqnarray}
Using equations (\ref{ybep1},\ref{ybep2}) and the YBE one  shows that the
matrices (\ref{fus1}-\ref{fus2}) satisfy a YBE where one space is a tensor
product of two spaces:
\begin{equation}
R^{(i)}_{<12>3}(\lambda-\mu) \, R^{(i)}_{<12>4}(\lambda) \,
R_{34}(\mu) = R_{34}(\mu) \,
R^{(i)}_{<12>4}(\lambda)\,  R^{(i)}_{<12>3}(\lambda-\mu)
\;\;,\;\;\; i=1,2 \label{ybefus1}
\end{equation}
Thus starting with a given solution of the YBE, we have obtained
higher-dimensional $R$-matrices which are also solutions
of the YBE. If $d_i, i=1,2,3$ are the dimensions of the spaces 1, 2 and 3,
then  $R^{(i)}_{<12>3}(\lambda)$ is a $d_1\times d_2 \times d_3$ dimensional
square matrix. However
the projection operators can be diagonalized simultaneously with
a change of basis matrix $S$. $S^{-1}_{12} R_{<12>3}^{(i)}(\lambda)\,
S_{12}$ also satisfy  equation (\ref{ybefus1}),
and their matrix expressions now contain
a  number of rows and columns with only vanishing elements, and  which can be
deleted without spoiling the Yang-Baxter property. The remaining
rows and columns can eventually be relabeled according to the
states of the corresponding representations.
Let ${\rm tr}( \pi^{(1)})= d$. Deleting the vanishing rows and columns from
$S^{-1}_{12} R^{(1)}_{<12>3}(\lambda)\, S_{12}$ and
$S^{-1}_{12} R^{(2)}_{<12>3}(\lambda)\, S_{12}$, yields
a $d\times d_3$ and  $(d_1\times  d_2 -d)\times d_3$ dimensional
square matrix, respectively.

It is possible to fuse two matrices $R_{<12>3}^{(i)}(\lambda)$
to obtain a matrix $R_{<12><34>}^{(i)}(\lambda)$. Setting $\mu=\rho$ in
(\ref{ybefus1}) and multiplying by the projection operators
yields two equations similar to (\ref{ybep1},\ref{ybep2}).
This leads to the following definitions:
\begin{eqnarray}
R^{(1)}_{<12><34>}(\lambda) &=&
\pi^{(1)}_{34}\, R_{<12>4}^{(1)}(\lambda+\rho)\, R_{<12>3}^{(1)}(\lambda)
\,\pi^{(1)}_{34}\label{fus3}\\
R^{(2)}_{<12><34>}(\lambda) &=&
\pi^{(2)}_{34}\, R_{<12>4}^{(2)}(\lambda+\rho)\, R_{<12>3}^{(2)}(\lambda) \,\pi^{(2)}_{34}\label{fus4}
\end{eqnarray}
Using the same methods as above one easily shows that these
matrices satisfy two Yang-Baxter equations ($i=1,2$):
\begin{eqnarray}
&R^{(i)}_{<12><34>}(\lambda-\mu) \, R^{(i)}_{<12>5}(\lambda) \,
R_{<34>5}^{(i)}(\mu) &\nonumber\\
& = R_{<34>5}^{(i)}(\mu)\, R^{(i)}_{<12>5}(\lambda)\,
R^{(i)}_{<12><34>}(\lambda-\mu)&\label{ybefus2}\\
&R^{(i)}_{<12><34>}(\lambda-\mu) \, R^{(i)}_{<12><56>}(\lambda) \,
R_{<34><56>}^{(i)}(\mu) &   \nonumber\\
&=  R_{<34><56>}^{(i)}(\mu)\, R^{(i)}_{<12><56>}(\lambda)\,
R^{(i)}_{<12><34>}(\lambda-\mu) & \label{ybefus3}
\end{eqnarray}
Again $S_{34}^{-1} R^{(i)}_{<12><34>}(\lambda) \, S_{34}$, $i=1,2$, still
satisfy the above YBE's. Removing by hand
a certain number of vanishing columns and rows, one
obtains matrices with smaller dimensions.

Assume  now  that the original $R$-matrix is  regular and unitary,
{\it i.e.}
\begin{equation}
R_{12}(0)= c\, {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{12}\;\;,\;\;\; R_{12}(\lambda)\, R_{21}(-\lambda)=
f(\lambda)\, {\Bbb I}\, \;\;,\label{regun}
\end{equation}
where ${\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}$ is the permutation operator.
The function $f(\lambda)$ is then even, and $c$ is an arbitrary non-vanishing
complex number.
The fused matrices (\ref{fus3},\ref{fus4}) inherit this property.
It is however necessary to correctly normalize them  for the corresponding
value of $c$ not to vanish. This is  achieved  by the following  normalization:
redefine $R_{<12><34>}^{(i)}(\lambda)$ as the right-hand side of
(\ref{fus3},\ref{fus4}) multiplied by  $\left( f(\lambda+\rho) \right)^{-1}$.
The reason for this normalization is the  vanishing of $f(\rho)$, for otherwise
the projector $R_{12}(\rho)$ would be invertible and therefore equal to
the trivial identity projector ${\Bbb I}$.

The limit $\lambda\rightarrow 0$ for the
redefined matrices (\ref{fus3}-\ref{fus4})
has to be taken with care.  Using the YBE one arrives at:
\begin{eqnarray}
R^{(1)}_{<12><34>}(0) &=&  -c^2\, {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13} {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24}\, S_{12}^{-1}\pi^{(1)}_{12}
S_{12}\, S_{34}^{-1} \pi^{(1)}_{34} S_{34}\label{regs1}\\
R^{(2)}_{<12><34>}(0) &=&  +c^2\, {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13} {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24}\, S_{12}^{-1}\pi^{(2)}_{12}
S_{12}\, S_{34}^{-1} \pi^{(2)}_{34} S_{34}\label{regs2}\\
R^{(i)}_{<12><34>}(\lambda)  R^{(i)}_{<34><12>}(-\lambda) &=& \left[ f(\lambda)\right]^2
S_{12}^{-1} \pi^{(i)}_{12} S_{12}\,
S_{34}^{-1} \pi^{(i)}_{34} S_{34}\;\;,\;\;\;
i=1,2\label{units}
\end{eqnarray}
where $R^{(i)}_{<34><12>}(\lambda)= {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13} {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24}\, R^{(i)}_{<12><34>}(\lambda)
\, {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13}{\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24}$.

Having obtained  regular solutions of the YBE, the usual procedure for
constructing integrable spin-chain Hamiltonians with short-range interaction
is by taking logarithmic  derivatives of the transfer matrices at $\lambda=0$.
The quadratic hamiltonian density of such integrable hierarchies is
nothing but the derivative at $\lambda=0$ of the matrix
$\check{R}(\lambda)={\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R} R(\lambda)$. Inclusion of  the normalizing factor gives:
\begin{eqnarray}
\check{R}^{(i)}_{<12><34>}(\lambda)&=& \frac{1}{f(\lambda+\rho)}
S_{12}^{-1} S_{34}^{-1} \pi_{12}^{(i)} \pi_{34}^{(i)}
R_{32}(\lambda+\rho) \check{R}_{13}(\lambda)\\
& & \times\check{R}_{24}(\lambda) R_{23}(\lambda-\rho)
\pi_{12}^{(i)} \pi_{34}^{(i)} S_{12} S_{34}\;\; ,\; i=1,2 \nonumber
\end{eqnarray}
Taking the limit $\lambda\rightarrow 0$, I find:
\begin{eqnarray}
\frac{d}{d\lambda}\check{R}^{(i)}_{<12><34>}(\lambda)_{|_0} &=&
- (\mp c^2)\frac{f''(0)}{2 f'(0)} \, S_{12}^{-1} \pi^{(i)}_{12}
S_{12}\, S_{34}^{-1} \pi^{(i)}_{34} S_{34} \nonumber\\
& &+ \frac{1}{2 f'(0)}  S_{12}^{-1} S_{34}^{-1} \pi^{(i)}_{12} \pi^{(i)}_{34}
\,\frac{d^2}{d\lambda^2}\left( R_{32}(\lambda+\rho) \check{R}_{13}(\lambda)
\right. \nonumber\\
& & \left.\times \check{R}_{24}(\lambda) R_{23}(\lambda-\rho)\right)_{|_0}\,
\pi^{(i)}_{12} \pi^{(i)}_{34} S_{12} S_{34} \label{hamden}
\end{eqnarray}
The two signs are as in the regularity equations above.
The first term is proportional to the identity  and may be dropped.

It is in fact possible to fuse an arbitrary product of  $R$ matrices to obtain solutions of the YBE corresponding to most representations of a given
Lie algebra. This was carried out in detail
for $sl(2)$ and $sl(3)$  in \cite{krs,kr}, and also  works
for the  other algebras \cite{kns}.

The above fusing scheme is now shown to work for the
multiplicity $A_{m-1}$ models.

\section{New integrable models}

As seen above, apart from satisfying the Yang-Baxter equation,
the projector property is the only additional ingredient
needed to construct fused matrices. In particular $R$ does not
have to correspond to a smallest representation to be able to
apply the fusion method.
The degeneration of the generically invertible  $R$-matrix
to a projector, for a certain value of the spectral parameter, is not
automatic. It is however a quite common property, especially for
the $R$-matrices based on Lie algebras.
For the models studied here, a quantum group structure does not
seem to exist, and one has to verify that a projector point exists.

I now apply this formalism to the models of \cite{amp}. This
will yield new matrices which define new integrable hierarchies.
The models of \cite{amp} are defined  as follows.
Take positive integers  $n_i$ and  $m$ such that
\begin{equation}
\sum_{i=1}^m n_i =n \;\;\;\;\;\;{\rm and}
\;\;\;\; 1\leq n_1 \leq ... \leq n_m \leq n -1
\end{equation}
The inequality restrictions avoid multiple counting of models, but
can otherwise be relaxed.
The set of  $n$ basis states  is the disjoint union of $m$  sets ${\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i$:
\begin{equation}
{\rm card}\,({\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i) = n_i \;\;,\;\;\; {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i \cap  {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j= \emptyset
\;\;\;\;{\rm for}\;\;\; i\not= j
\end{equation}
${\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i$ should not be confused with the Lie algebra $sl(i+1)$.
Let $E^{\alpha\beta}$ be a square matrix  with a one at row $\alpha$
and column $\beta$ and zeros otherwise.
Define   the following operators:
\begin{eqnarray}
\tilde{P}^{(+)}&=& \sum_{1\leq i< j \leq m}\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j} E^{\alpha_j\alpha_i}\otimes E^{\alpha_i\alpha_j} \label{pm}\\
\tilde{P}^{(-)}&=& \sum_{1\leq i< j \leq m}\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j} E^{\alpha_i\alpha_j}\otimes E^{\alpha_j\alpha_i} \label{pp}\\
\tilde{P}^{(3)}&=&\sum_{1\leq i< j \leq m}\;\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j} \left(x E^{\alpha_j\alpha_j}\otimes E^{\alpha_i\alpha_i}
+ x^{-1} E^{\alpha_i\alpha_i}\otimes E^{\alpha_j\alpha_j}\right) \\
\end{eqnarray}
The twist parameters were taken equal to one arbitrary complex parameter $x$.
Let $y=e^{i\lambda}$ and $q=e^{i\gamma}$, where $\lambda$ is the spectral
parameter and $\gamma$ the quantum  parameter.
The $R$-matrix  is then given by:
\begin{eqnarray}
&R(\lambda)= {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}\, \sin(\lambda+\gamma) + \tilde{P}\, \sin\lambda &\label{ram}\\
&\tilde{P}\equiv \tilde{P}^{(3)} -(q^{-1}\, \tilde{P}^{(+)} +
q\, \tilde{P}^{(-)}) &
\end{eqnarray}
This model is  denoted by $(n_1, ... , n_m;m,n)$.
For $n=m$  and $x=1$
one obtains  the $A_{m-1}$ $R$-matrix of \cite{jimbo}.
$R(\lambda)$ is  regular and unitary:
\begin{eqnarray}
&R_{12}(0)={\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{12}\,\sin\gamma &\label{regu}\\
& R_{12}(\lambda)\, R_{21}(-\lambda)={\Bbb I}\,
f(\lambda)={\Bbb I}\,\sin(\gamma+\lambda) \sin(\gamma-\lambda) &\label{unit}
\end{eqnarray}
where $R_{21}(\lambda)={\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{12}\, R_{12}(\lambda)\, {\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{12}$. As seen in section
\ref{fusionsec}, these properties are
inherited by some of the  fused matrices.

The right-hand side of   (\ref{unit}) shows that $\lambda=\pm \gamma$
are possible projector points. Further checks show that
matrix (\ref{ram}) yields a projector at $\lambda=\rho=-\gamma$:
$R(-\gamma)= -\tilde{P}\sin\gamma $. Let
\begin{equation}
\pi^{(1)}=\frac{1}{x+x^{-1}} \tilde{P} \;\; ,\;\;\;
\pi^{(2)}={\Bbb I}-\pi^{(1)} \label{proj}
\end{equation}
One has: $(\pi^{(i)})^2=\pi^{(i)}$, $i=1,2$,  and
$\pi^{(1)}\pi^{(2)}=\pi^{(2)}\pi^{(1)}=0$.
The dimensions of these projectors are given by their traces:
\begin{eqnarray}
{\rm tr}\,(\pi^{(1)}) &=& \sum_{i<j} n_i \, n_j = \frac{1}{2} \left(
n^2- \sum_i (n_i)^2 \right) \\
{\rm tr}\,(\pi^{(2)}) &=& n^2 - \sum_{i<j} n_i\,  n_j = \frac{1}{2} \left(
n^2+ \sum_i (n_i)^2 \right)
\end{eqnarray}
The matrix $S$ which diagonalizes $\pi^{(1)}$ and $\pi^{(2)}$ is given by:
\begin{eqnarray}
S&=& \sum_{i=1}^{m} \sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i} \sum_{\beta_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
E^{\alpha_i\alpha_i}\otimes E^{\beta_i\beta_i}\nonumber\\
& & +\sum_{1\leq i< j \leq m}\;\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j} \left( E^{\alpha_i\alpha_i}\otimes E^{\alpha_j\alpha_j}
-\frac{x}{q} E^{\alpha_j\alpha_j}\otimes E^{\alpha_i\alpha_i}\right)\nonumber\\
& &+\sum_{1\leq i< j \leq m}\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j}\left( E^{\alpha_i\alpha_j}\otimes E^{\alpha_j\alpha_i}
+\frac{1}{x q} E^{\alpha_j\alpha_i}\otimes E^{\alpha_i\alpha_j}\right)\label{ss}\\
S^{-1}&=&\sum_{i=1}^{m} \sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i} \sum_{\beta_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
E^{\alpha_i\alpha_i}\otimes E^{\beta_i\beta_i}\nonumber\\
& & +\frac{q}{x+x^{-1}}\sum_{1\leq i< j \leq m}\;\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j} \left( \frac{x}{q}E^{\alpha_i\alpha_i}\otimes E^{\alpha_j\alpha_j}
- E^{\alpha_j\alpha_j}\otimes E^{\alpha_i\alpha_i}\right)\nonumber\\
& & +\frac{q}{x+x^{-1}}\sum_{1\leq i< j \leq m}\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j}\left( E^{\alpha_i\alpha_j}\otimes E^{\alpha_j\alpha_i}
+\frac{1}{x q} E^{\alpha_j\alpha_i}\otimes E^{\alpha_i\alpha_j}\right)\label{ss1}
\end{eqnarray}
The diagonalized projectors then read
\begin{eqnarray}
S^{-1}\, \pi^{(1)}\, S &=& \sum_{1\leq i< j \leq m}\;\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j}  E^{\alpha_j\alpha_j}\otimes E^{\alpha_i\alpha_i}\\
S^{-1}\, \pi^{(2)}\, S &=&  \sum_{i=1}^{m} \sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\beta_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i} E^{\alpha_i\alpha_i}\otimes E^{\beta_i\beta_i}\nonumber\\
& & +\sum_{1\leq i< j \leq m}\;\sum_{\alpha_i \in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_i}
\sum_{\alpha_j\in {\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_j}  E^{\alpha_i\alpha_i}\otimes E^{\alpha_j\alpha_j}
\end{eqnarray}
The explicit expressions of the four fused matrices $R^{(i)}_{<12>3}$ and
$R^{(i)}_{<12><34>}$ can be found by straightforward if tedious
expansions of the products in (\ref{fus1},\ref{fus2},\ref{fus3},\ref{fus4}),
using the explicit expressions (\ref{ram},\ref{proj},\ref{ss},\ref{ss1}).
Similarly, the quadratic hamiltonian density
is obtained by replacing the matrices in (\ref{hamden}) and expanding
the products.

The following point is worth mentioning.
Since $R_{12}(-\gamma) \, R_{21}(\gamma) =0$, it may seem that
the complementary projector $\pi^{(2)}$ is proportional to $R_{21}(\gamma)$.
However this is generically {\it not} the case.
It is true only when all the $n_i$ are equal to one and $x=q^{\pm 1}$.
This is another distinguishing feature of the $n_i \not= 1$ models.

\section{Some $sl(2)$ models}\label{sl2}

Consider now the   $m=2$ case, {\it i.e.} the XXC models \cite{xxc}.
They have an underlying $sl(2)$ structure.  Their $R$ matrix
is just the multistate version of the one  corresponding to
the spin-$\frac{1}{2}$ model $(n_1=n_2=1)$.

Tedious but simple calculations lead to the
following matrix which carries  spin-0$\times$spin-$\frac{1}{2}$:
\begin{eqnarray}
R_{<12>3}^{(1)}(\lambda)&=& \sin\lambda \;\sin
(\lambda+2\gamma)\times \label{rm012}\\
& &\left(\sum_{\alpha_1,\beta_1} \sum_{\alpha_2}
x\, E^{\alpha_2\alpha_2} \otimes E^{\beta_1\alpha_1}\otimes E^{\alpha_1\beta_1}
+\sum_{\alpha_1}\sum_{\alpha_2,\beta_2} x^{-1} E^{\beta_2\alpha_2}\otimes E^{\alpha_1\alpha_1}
\otimes E^{\alpha_2\beta_2} \right)\nonumber
\end{eqnarray}
The dimension of this matrix is $n_1\, n_2 \, n$, as expected.
The corresponding two-dimensional vertex model has $n_1\, n_2$ possible
states on, {\it e.g.}, the horizontal
links and $n$ states on the vertical links.

Note that the $x+x^{-1}$ denominator has dropped out of the final result and
therefore $R$ is defined for all finite values of $x$, including $x=\pm i$.
This also holds for the three  fused matrices given below.

The matrix which carries  spin-0$\times$spin-0 can then be obtained:
\begin{eqnarray}
R_{<12><34>}^{(1)}(\lambda)&=& \frac{\sin(\lambda-\gamma)
\sin(\lambda+\gamma)\sin(\lambda+2\gamma)}{\sin(2\gamma-\lambda)}
\sum_{\alpha_1,\beta_1} \sum_{\alpha_2,\beta_2}
E^{\alpha_2\beta_2}\otimes  E^{\alpha_1\beta_1}\otimes
E^{\beta_2\alpha_2}E^{\beta_1\alpha_1}\nonumber\\
& =& \frac{\sin(\lambda-\gamma)
\sin(\lambda+\gamma)\sin(\lambda+2\gamma)}{\sin(2\gamma-\lambda)}\;
{\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13}^{({\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_2)} \,{\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24}^{({\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_1)}\label{rm00}
\end{eqnarray}
${\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13}^{({\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_2)}$ and  ${\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24}^{({\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_1)}$ are the permutation
operators in the subspaces ${\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_2$ and ${\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_1$, respectively.
The dimension of this matrix is $(n_1 n_2)^2$, as it should be.
It satisfies the regularity and unitarity properties (\ref{regs1},\ref{units}).
Here the vertex model has $n_1\, n_2$ possible states on both
the horizontal and vertical links.
The resulting spin-chain is however rather trivial as the $\lambda$-dependence can
be normalized away, and the operator part yields $S_{12}^{-1}\pi_{12}^{(1)}
S_{12}\, S_{34}^{-1}\pi_{34}^{(1)} S_{34}$, {\it i.e.}
the identity operators in  the spin-0 subspaces.

The matrix carrying spin-1$\times$spin-$\frac{1}{2}$ is:
\begin{eqnarray}
\frac{1}{\sin(\lambda+\gamma)}\, R_{<12>3}^{(2)}(\lambda) & =& +\sin(\lambda+2\gamma)
\sum_{\alpha_1,\beta_1,\gamma_1} E^{\alpha_1\beta_1}\otimes
E^{\gamma_1\alpha_1}\otimes E^{\beta_1\gamma_1}\label{rm112}\\
& & + \sin(\lambda+2\gamma) \sum_{\alpha_2,\beta_2,\gamma_2}
E^{\alpha_2\beta_2}\otimes E^{\gamma_2\alpha_2}\otimes E^{\beta_2\gamma_2}\nonumber\\
& & +y \,\sin(2\gamma) \sum_{\alpha_1}\sum_{\alpha_2,\beta_2}
E^{\alpha_2\alpha_1}\otimes E^{\beta_2\alpha_2} \otimes E^{\alpha_1\beta_2}\nonumber\\
& & +q\, y \,\sin\gamma \, \sum_{\alpha_1,\beta_1}\sum_{\alpha_2}
E^{\beta_1\alpha_1}\otimes E^{\alpha_2\beta_1} \otimes E^{\alpha_1\alpha_2}\nonumber\\
& & + x\, \sin(\lambda+\gamma) \sum_{\alpha_1,\beta_1}\sum_{\alpha_2}
E^{\beta_1\alpha_1}\otimes E^{\alpha_2\alpha_2}\otimes  E^{\alpha_1\beta_1}\nonumber\\
& & + x^{-1} \sin(\lambda+\gamma) \sum_{\alpha_1}\sum_{\alpha_2,\beta_2}
E^{\alpha_1\alpha_1}\otimes E^{\beta_2\alpha_2}\otimes E^{\alpha_2\beta_2}\nonumber\\
& & +x \, y^{-1} \sin \gamma \, \sum_{\alpha_1}\sum_{\alpha_2,\beta_2}
E^{\alpha_1\alpha_2}\otimes E^{\beta_2\beta_2} \otimes E^{\alpha_2\alpha_1}\nonumber\\
& & + x^{-1} q^{-1} y^{-1} \sin(2\gamma) \sum_{\alpha_1,\beta_1}\sum_{\alpha_2}
E^{\alpha_1\alpha_1}\otimes E^{\beta_1\alpha_2}\otimes  E^{\alpha_2\beta_1}\nonumber\\
& & + x^2 \sin\lambda \, \sum_{\alpha_1}\sum_{\alpha_2,\beta_2}
E^{\alpha_2\alpha_2}\otimes E^{\beta_2\beta_2} \otimes E^{\alpha_1\alpha_1}\nonumber\\
& & + x^{-2} \sin\lambda\, \sum_{\alpha_1,\beta_1}\sum_{\alpha_2}
E^{\alpha_1\alpha_1}\otimes E^{\beta_1\beta_1}\otimes E^{\alpha_2\alpha_2}\nonumber
\end{eqnarray}
The vertex model model has $(n_1)^2 + (n_2)^2 +n_1\, n_2$ states on
the horizontal links and $n$ states on the vertical links.

The preceding matrix is then used to find the spin-1$\times$spin-1 matrix:
\begin{eqnarray}
\frac{\sin(2\gamma-\lambda)}{\sin(\lambda+\gamma)}&\times &
R_{<12><34>}^{(2)}(\lambda) =\label{rm11}\\
& & +\sin(\lambda+\gamma) \sin(\lambda+2\gamma)
\sum_{\alpha_1,\beta_1,\gamma_1,\delta_1} E^{\alpha_1\beta_1}\otimes
E^{\gamma_1\delta_1}\otimes E^{\beta_1\alpha_1}\otimes
E^{\delta_1\gamma_1}\nonumber\\
& & +\sin(\lambda+\gamma) \sin(\lambda+2\gamma)
\sum_{\alpha_2,\beta_2,\gamma_2,\delta_2} E^{\alpha_2\beta_2}\otimes
E^{\gamma_2\delta_2}\otimes E^{\beta_2\alpha_2}\otimes E^{\delta_2\gamma_2}\nonumber\\
& & +y \sin(2\gamma)\sin(\lambda+\gamma)
\sum_{\alpha_1}\sum_{\alpha_2,\beta_2,\gamma_2} E^{\alpha_2\alpha_1}\otimes
E^{\beta_2\gamma_2}\otimes E^{\alpha_1\alpha_2}\otimes E^{\gamma_2\beta_2}\nonumber\\
& & +y^{-1} \sin(2\gamma)\sin(\lambda+\gamma)
\sum_{\alpha_1,\beta_1,\gamma_1}\sum_{\alpha_2} E^{\alpha_1\beta_1}\otimes
E^{\gamma_1\alpha_2}\otimes E^{\beta_1\alpha_1}\otimes E^{\alpha_2\gamma_1}\nonumber\\
& & +y \sin(2\gamma)\sin(\lambda+\gamma)
\sum_{\alpha_1,\beta_1,\gamma_1}\sum_{\alpha_2} E^{\alpha_1\beta_1}\otimes
E^{\alpha_2\gamma_1}\otimes E^{\beta_1\alpha_1}\otimes E^{\gamma_1\alpha_2}\nonumber\\
& & +y^{-1} \sin(2\gamma)\sin(\lambda+\gamma)
\sum_{\alpha_1}\sum_{\alpha_2,\beta_2,\gamma_2} E^{\alpha_1\alpha_2}\otimes
E^{\beta_2\gamma_2}\otimes E^{\alpha_2\alpha_1}\otimes E^{\gamma_2\beta_2}\nonumber\\
& & +(\sin\gamma \sin(2\gamma)+\sin\lambda\sin(\lambda+\gamma))
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_1\beta_1}\otimes
E^{\alpha_2\beta_2}\otimes E^{\beta_1\alpha_1}\otimes E^{\beta_2\alpha_2}\nonumber\\
& & +y^2 \sin\gamma\sin(2\gamma)
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_2\alpha_1}\otimes
E^{\beta_2\beta_1}\otimes E^{\alpha_1\alpha_2}\otimes E^{\beta_1\beta_2}\nonumber\\
& & +y^{-2} \sin\gamma\sin(2\gamma)
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_1\alpha_2}\otimes
E^{\beta_1\beta_2}\otimes E^{\alpha_2\alpha_1}\otimes E^{\beta_2\beta_1}\nonumber\\
& & +2 x \, q^{-1} y\cos\gamma \sin(2\gamma)\sin\lambda\,
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_2\alpha_1}\otimes
E^{\beta_2\alpha_2}\otimes E^{\alpha_1\beta_1}\otimes E^{\beta_1\beta_2}\nonumber\\
& & +x^{-1} q\, y \sin\gamma\sin\lambda\,
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_1\beta_1}\otimes
E^{\alpha_2\alpha_1}\otimes E^{\beta_1\beta_2}\otimes E^{\beta_2\alpha_2}\nonumber\\
& & +x^2 \sin\lambda\sin(\lambda+\gamma)
\sum_{\alpha_1,\beta_1,\gamma_1}\sum_{\alpha_2} E^{\alpha_1\beta_1}\otimes
E^{\alpha_2\alpha_2}\otimes E^{\beta_1\gamma_1}\otimes E^{\gamma_1\alpha_1}\nonumber\\
& & +x^2 \sin\lambda\sin(\lambda+\gamma)
\sum_{\alpha_1}\sum_{\alpha_2,\beta_2,\gamma_2} E^{\alpha_2\beta_2}\otimes
E^{\gamma_2\alpha_2}\otimes E^{\alpha_1\alpha_1}\otimes E^{\beta_2\gamma_2}\nonumber\\
& & +x^{-2} \sin\lambda\sin(\lambda+\gamma)
\sum_{\alpha_1,\beta_1,\gamma_1}\sum_{\alpha_2} E^{\alpha_1\beta_1}\otimes
E^{\gamma_1\alpha_1}\otimes E^{\beta_1\gamma_1}\otimes E^{\alpha_2\alpha_2}\nonumber\\
& & +x^{-2} \sin\lambda\sin(\lambda+\gamma)
\sum_{\alpha_1}\sum_{\alpha_2,\beta_2,\gamma_2} E^{\alpha_1\alpha_1}\otimes
E^{\alpha_2\beta_2}\otimes E^{\beta_2\gamma_2}\otimes E^{\gamma_2\alpha_2}\nonumber\\
& & +x^3 q \, y^{-1} \sin\gamma\sin\lambda\,
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_1\alpha_2}\otimes
E^{\beta_2\beta_2}\otimes E^{\beta_1\beta_1}\otimes E^{\alpha_2\alpha_1}\nonumber\\
& & +2 x^{-3} q^{-1} y^{-1} \cos\gamma \sin(2\gamma)\sin\lambda\,
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_1\alpha_1}\otimes
E^{\beta_1\alpha_2}\otimes E^{\alpha_2\beta_1}\otimes E^{\beta_2\beta_2}\nonumber\\
& & +x^4 \sin(\lambda-\gamma)\sin\lambda\,
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_2\alpha_2}\otimes
E^{\beta_2\beta_2}\otimes E^{\alpha_1\alpha_1}\otimes E^{\beta_1\beta_1}\nonumber\\
& & +x^{-4} \sin(\lambda-\gamma)\sin\lambda\,
\sum_{\alpha_1,\beta_1}\sum_{\alpha_2,\beta_2} E^{\alpha_1\alpha_1}\otimes
E^{\beta_1\beta_1}\otimes E^{\alpha_2\alpha_2}\otimes E^{\beta_2\beta_2}\nonumber
\end{eqnarray}
This matrix does satisfy  the regularity and unitarity properties
(\ref{regs2},\ref{units}).
The number of states on both the horizontal and vertical links is
now $(n_1)^2 + (n_2)^2 +n_1\, n_2$.

The four matrices (\ref{rm012},\ref{rm00},\ref{rm112},\ref{rm11}) have
2, 1, 10, 19 types of terms, respectively. This was expected from the
$S^z$ conservation  of $sl(2)$.
When $n_1=n_2=1$  the matrices give the
$sl(2)$ 2-, 1-, 10-, 19-vertex models. The latter two models can be found
in \cite{fzmod,ppny,mene2}. To carry out a comparison
it is necessary to relabel
the states so that $R$ looks like an operator acting on the tensor
product of two spaces: $R=\sum E\otimes E$.
For instance, in (\ref{rm112}), with ${\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_1=\{ 1\}$, ${\cal A}}       \def\CB{{\cal B}}       \def\CC{{\cal C}_2=\{ 2\}$, one can
take the matrix element  $\sin(\lambda+\gamma) \sin(\lambda+2\gamma) E^{11}\otimes
E^{11}\otimes E^{11}$ to correspond to $|+1\rangle |+\frac{1}{2}\rangle\times
|+1\rangle |+\frac{1}{2}\rangle$, and
$(x\, q\, y)^{-1}\sin(2\gamma)\sin(\lambda+\gamma) E^{11}\otimes E^{12}\otimes
E^{21}$ to $|+1\rangle |-\frac{1}{2}\rangle\times
|0\rangle |+\frac{1}{2}\rangle$.
The matrix (19) of reference \cite{mene2}
can be obtained by fusing the symmetric form of the $sl(2)$ $R$-matrix
\cite{xxc}. It is also necessary to do a gauge transformation after fusing,
in order to render the resulting matrix completely symmetric.
This introduces the unusual square-root element $d$ of that
reference. Finally, let  $u=\lambda+\eta/2$ and $\eta=\gamma$ to complete the
identification. Similar remarks apply to the identification
of the 19-vertex models.

The interpretation of the multiple-states in terms of $sl(2)$ states is
simple. Recall first that for  the models (\ref{ram})
with $m=2$, the interpretation is:
\begin{equation}
{\rm state}(\alpha_1)  \longleftrightarrow
|+\frac{1}{2}\rangle_{\alpha_1}\quad ,\quad
{\rm state}(\alpha_2)  \longleftrightarrow |-\frac{1}{2}\rangle_{\alpha_2}
\end{equation}
This yields the following identifications when two spin-$\frac{1}{2}$
spaces are fused:
\begin{equation}
{\rm state}(\alpha_2\alpha_1)  \longleftrightarrow |0\rangle_{\alpha_2\alpha_1}\quad
, \quad n_1\, n_2
\end{equation}
for the spin 0 representation obtained from $\pi^{(1)}$, and
\begin{eqnarray}
& & {\rm state}(\alpha_1\beta_1)  \longleftrightarrow |+1\rangle_{\alpha_1\beta_1}
\quad , \quad (n_1)^2 \\
& & {\rm state}(\alpha_1\alpha_2)  \longleftrightarrow |0\rangle_{\alpha_1\alpha_2}
\quad , \quad n_1\, n_2 \\
& & {\rm state}(\alpha_2\beta_2)  \longleftrightarrow |-1\rangle_{\alpha_2\beta_2}
\quad , \quad (n_2)^2
\end{eqnarray}
for the spin 1 representation obtained from $\pi^{(2)}$.
The numbers on the right are the number of states of the corresponding type.
Whereas the numbers of copies of the states $|\pm 1\rangle$ are
uncorrelated, $(n_1)^2$ and $(n_2)^2$, the number of states
of type $|0\rangle$ has to be $n_1\, n_2$.
Thus  a naive trial to obtain the multistate version
of the spin-1$\times$spin-1 model would have failed. Fusion gives the
correct answer.

The first derivative at $\lambda=0$ of  $\check{R}^{(2)}_{<12><34>}(\lambda)=
{\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{13}{\cal P}}       \def\CQ{{\cal Q}}       \def\CR{{\cal R}_{24} R^{(2)}_{<12><34>}(\lambda)$, for
the matrix  of (\ref{rm11}), gives the hamiltonian density $H_{ii+1}$
for the multistate  version of the spin-1 model.
The $n_1=n_2=1$ Hamiltonian is also  known as the Fateev-Zamolodchikov
model \cite{fzmod}.

\section{Concluding remarks}

The multiplicity $A_{m-1}$ models  were shown to allow fusion and
multistate models were  obtained for higher dimensional representations.
The spin-0 and spin-1 models were derived explicitly. This provided in
particular the generalization  of the Fateev-Zamolodchikov model.

The underlying $sl(m)$ structure of these models was justified in
\cite{amp}. It provides a natural way to
label them in terms of $sl(m)$ representations. This language has been used
throughout the paper and in particular in  section \ref{sl2}.
I recall here
the main points in view of an extension to the higher dimensional models
just obtained.
The matrices  (\ref{ram}) have the  following  structure:
$R(\lambda)=\sum_k g_k(\lambda) \CO_k$, where all the spectral parameter dependence
is contained in the functions $g_k(\lambda)$. The operators $\CO_k$ may depend
on the other parameters. Replacing $R$ in the YBE's it is required to
satisfy,  and identifying the
coefficients of the linearly independent functions yield a set of equations
for the operators $\CO_k$, where the spectral parameters do not appear.
In the case of the $\check{\CO}_k$ of (\ref{ram}) one  has simple
$n_i$-independent trigonometric  functions,  and obtains
the Hecke algebra, for all values of the $n_i$'s, and
in particular for $n_i=1$. This and the fact that the operators have the same
structure as for $n_i=1$ shows that one has the natural generalization.
The algebraic Bethe Ansatz was also found to be  based on the
Dynkin diagram of  $A_{m-1}$. Thus the
functional {\it and} operatorial structures
of $R(\lambda)=\sum_k g_k(\lambda) \CO_k$ are the same as for $n_i=1$.
The quite general  fusion construction reviewed in section
\ref{fusionsec} preserves   the functional and algebraic structures.
Therefore one again has the natural multistate generalization for
the higher dimensional representations.

The rational limit of all the matrices considered above exist and provide
rational  solutions to the various Yang-Baxter equations.
This limit is obtained by rescaling $\lambda$ to $\gamma \lambda$, and
dividing  by  an appropriate power of $\gamma$ or $\sin\gamma$  in
order to obtain a finite limit.

The  models (\ref{ram}) have extended symmetries \cite{amp}:
$sl(n_1)\oplus ...\oplus sl(n_m)\oplus u(1)
\oplus ... \oplus u(1)$. It is obvious that the higher dimensional
models inherit similar symmetries.
These are related to the
existence of many states of a same type, as seen in the
spin-0  and spin-1 examples. Most (but not all) diagonal operators
commute with the $R$-matrix, as they either correspond to $u(1)$ charges of
states of the same type, or to realizations of $S^z$.
The non-diagonal operators which commute with
the $R$-matrix are those which acts within the space spanned by
a state and its copies.

These symmetries will also be reflected in a diagonalization by Bethe
Ansatz, as happened for the fundamental models \cite{amp}.
The diagonalization makes use of the standard techniques associated
with higher dimensional representations. In particular, it uses
fusion to find relations between the various transfer matrices.

redpajama_set_name: RedPajamaArXiv


text:
Niagara's Hidden History
Ginger Strand
Some of the most compelling stories about New York's famous natural wonder have been either forgotten or deliberately ignored. But archives have revealed some secrets.
Hotel Revolution
A.J. Schenkman
Location, location, location: the house of Jonathan and Tryntje Hasbrouck in Newburgh was in great demand during the Revolution, especially by General George Washington.
The Rescue of Charles Nalle
Scott Christianson
A fugitive slave was liberated, not captured, in upstate New York just before the Civil War, with the help of an outraged populace and Underground Railroad conductor Harriet Tubman.
A Woman of Colorful Means
Jane Lancaster
Madame Eliza Jumel was a wealthy and independent woman who seemed not to know her place in nineteenth-century Saratoga society––but what a place it was.
Ted Merwin
The New York Jewish delicatessen is as much a symbol of the Big Apple as any tourist attraction––and offers a far more personal experience. But how many are left?
Niagara's Hidden History
By Ginger Strand
Niagara Falls is one of America's best-known natural wonders. Scholars have expounded on its role in shaping the American sublime, popular histories have recounted its capacity for power development, and souvenir volumes regularly recount tales of daredevils and honeymoons. The image of the Falls has graced everything from masterpieces of landscape painting to tea towels, from early Lumière Brothers films to blockbuster IMAX movies. A depiction of the Falls even occupies one corner of New York's license plates, opposite the New York City skyline: landscape and cityscape, the state's two must-see sights. Yet the most interesting features of this icon's history have remained hidden—sometimes forgotten, sometimes deliberately ignored. My search for this hidden history led me to numerous archival collections—each of which, it seemed, yielded up another surprising story.
Beauty and Power
One of the most common tales told about Niagara Falls is that the family of Augustus Porter, who founded the town of Niagara Falls, kept the area around the falls in its natural state until the State of New York bought it in 1885. But letters between Augustus and his brother, Peter, founder of the town of Black Rock just upstream, show that this was far from the case. The Porters developed the Niagara environs to the best of their ability. In the 1820s and 1830s they built snack stands and viewing platforms, grist mills and tanneries, and even planned to build a large hotel for wealthy patrons on Goat Island, which separates the Canadian Horseshoe Falls from the American Falls. They also attempted, at least twice, to sell all their land at Niagara to wealthy "capitalists," as they called them. They ran newspaper ads touting the potential water power to be had from the Falls.
After the Civil War, well heeled and well-connected gentlemen began appealing to the state to buy the area around the Falls. The movement, known as "Free Niagara," was spearheaded by Frederick Law Olmsted, the famous landscape architect. Luminaries like J.P. Morgan, Oliver Wendell Holmes, John Jay, Thomas Carlyle, and John Ruskin signed a petition urging the creation of a state park at Niagara. They were successful in 1885. But left out of the story of a public minded movement is the profit motive that drove it. Many of the same men who signed Olmsted's petition turned up on the board of the Niagara Falls Power Company, which succeeded, ten years later, in harnessing the Falls for electricity. In fact, Thomas Evershed, who surveyed the land around the Falls and drew up the map of the proposed state park, was the company's engineer. History has painted him as a savior of Niagara's beauty, but he was also thinking of money; Evershed's map, which exists only in two hand-drawn versions, shows how he carefully drew the boundaries of the state park so that they wouldn't interfere with the canals required to harness Niagara's power. After the state park was established, the Falls was quickly harnessed, beginning a new industrial age at Niagara.
Mummies and Two-Headed Calves
For many years, the Niagara Falls Museum was an attraction rivaled only by the waterfall itself. Built at the brink of the Horseshoe Falls, the museum was owned by Thomas Barnett and his family, a museum clan dedicated to the study of natural history and the pursuit of exotic specimens. Their collections included plants, minerals, shells, and mounted birds and animals. Like many museums of the time, they also had a collection of "freaks of nature," including a two-headed calf and a two-legged dog.
In the 1850s, the Barnetts acquired a group of Egyptian mummies that quickly became a featured exhibit at the museum, but shortly thereafter the family fell on hard times and lost possession of the collections they had built for years. Those collections passed through several families' ownership and ended up, in 1999, in the hands of a Toronto shrunken-head collector named Billy Jamieson, who sold the mummies to an American museum for a hefty sum. To the shock of the antiquities world, one of the mummies turned out to be a pharaoh—Rameses I, founder of the New Kingdom's 19th Dynasty.
Jamieson realized the mummy might have been a pharaoh because a diary recorded its purchase. Dr. James Douglas, a Montreal physician, had traveled to Egypt with Sidney Barnett, Thomas Barnett's son, and in his travel journal Douglas related how he and Barnett had bought a mummy from an Egyptian antiquities dealer named Mustapha Aga Ayat. Mustapha was a well-known "fence" for a family of tomb robbers who had discovered a cache of royal artifacts in the cliffs of Deir el-Bahri. When the robbers were finally caught, authorities discovered the coffin of Rameses I in the tomb they had plundered. It was empty.
For decades, rumors persisted that a pharaoh lay among the artifacts at the Niagara Falls Museum, but no one could believe it. A royal mummy lying just steps away from a two-headed calf? Only when the Michael Carlos Museum of Emory University bought the mummies and began analyzing them using CAT scans and computer imaging was the rumor taken seriously. Egypt's top antiquities expert examined the mummy and declared it to be a pharaoh, at which point it was returned to Egypt. Thus with the help of a simple diary, another of Niagara's secrets was brought to light.
Icon of Fugitives
A little-known highlight of Niagara's history is its role in the Underground Railroad. In the years leading up to the Fugitive Slave Act of 1850, slave catchers became increasingly active in northern states, and fleeing slaves began heading to Canada, where slavery was illegal. One of the key places to cross into Canada was the Niagara region. There were rail connections to the Falls, and the area was well known; many southerners even took their slaves with them when they went there on vacation.
Before 1848, when the first bridge across the river was completed, boats could be hired to cross the river into Ontario. At Black Rock, the river narrowed enough that some fugitives even attempted to swim across. As national dissent over slavery grew, fugitives by the hundreds crossed at Niagara to Canada, often helped by African American workers in Niagara's restaurants and hotels. Harriet Tubman, who lived in nearby St. Catharines, personally led scores of people through Niagara Falls to freedom.
Peter B. Porter, Black Rock's founder, watched all of this with dismay. He was a hero from the War of 1812 and was now a militia general. He had served in Congress and as John Quincy Adams's secretary of war. He had also married into a prominent, slave-owning Kentucky family and even inherited twenty-five slaves himself. In fact, it's one of Niagara's most surprising secrets that General Porter, one of Niagara's town fathers, aided and abetted slave catchers who came to Niagara to "retrieve" fugitives. He even helped spark Canada's first race riot when he assisted a man, David Castleman, who attempted to extradite a fugitive named Solomon Mosby from Canada in 1837.
Castleman stayed with Porter while petitioning Ontario's provincial governor for extradition. When the governor agreed and Mosby was arrested at Niagara-on-the- Lake, people began to gather outside the jail. As the deputy sheriff attempted to take Mosby to the ferry for extradition, an angry mob intervened and freed him. In the melee, two protesters were killed. Peter Porter wrote an angry letter to the governor after the incident, but it fell on deaf ears. In fact, the case only fueled Canada's strong abolitionist stance. The following year, the British government upheld Canada's decision not to extradite fugitive slaves to the United States.
Coded Spectacles
In sharp contrast with the Underground Railroad, there's no shortage of stories about aerialist Blondin's famous tightrope ascensions over the Niagara Gorge. Blondin is frequently mentioned in Niagara histories, but the significance of his performances isn't. In 1859 and 1860, as civil war looked inevitable, Blondin's spectacular crossings of the falls referenced the Underground Railroad through a series of codes. He crossed his tightrope dressed as a chef or a day laborer—jobs typically held by African Americans; he crossed shackled and with a sack over his head; he crossed in the dark of night; and he even famously crossed with his manager on his back. All of this transpired just a few yards downstream from the bridge that actual fugitives regularly crossed at night as they risked being dragged back to the South in shackles. The meaning of Blondin's performances was made nearly explicit in the magazines of the times: cartoons in Harper's and Vanity Fair depicted President Lincoln as Blondin, crossing a tightrope over Niagara Falls with a slave on his back. These cartoons, as well as accounts of Blondin's performances, helped me decode the secret rhapsody to freedom behind Blondin's apparent acts of pure spectacle.
The Waterfall and the Bomb
Not all of Niagara's secrets are quite so far in the past. During World War II, Niagara Falls was critical to the building of the atomic bomb. This secret was successfully kept not only from the public, but from the laborers who did the work. Only in the 1990s did the truth begin to emerge: the government had hired dozens of private contractors to quietly conduct experiments to refine and roll uranium for the Manhattan Project. With its concentration of chemical and electro-metallurgical plants, Niagara Falls was home to many of these contractors. The effects of their work are still present today; for example, the Army Corps of Engineers is cleaning up seven radioactive sites within ten miles of Niagara Falls through a program known as FUSRAP (Formerly Used Sites' Remedial Action Program). The Corps's extensive documentation of the sites' histories and cleanup efforts, deposited in local archives, ensures that another piece of Niagara's hidden history will be made available to the public, now and in the future.


As we near the end of our crop, we wanted to go back to military/patriotic theme again. This altered item was created by Carolyn, SL DTM and she used the Military line from Karen Foster Design.
Again, this challenge is to create anything patriotic in honor of our military personnel, whether it be more cards to mail in to provide them cards to send home or thanking them for their service, or something for someone you know who is/has served our country and your freedom.


text:
Kyrgyzstan: Prosecutors use 2010 ethnic unrest as cudgel against gover
Kyrgyzstan: Prosecutors use 2010 ethnic unrest as cudgel against government opponents
When Kyrgyzstan's president seized power in 2020, he pledged that the era of political witch-hunts had come to an end.
Sadyr Japarov had himself served time in prison, for what he insists were unfair charges of kidnapping, and he said he didn't want the same done to others.
It turns out that he may not have been entirely sincere.
On May 20, the office of the Prosecutor General announced that it was filing a case of abuse of office against three members of a provisional cabinet formed after political unrest toppled the government in April 2010. Supporters of Keneshbek Dushebayev, a former head of the security services, Ismail Isakov, an ex-defence minister, and Bektur Asanov, once the governor of the southern Jalal-Abad region, all of them critics of the Japarov administration, say the probe is "motivated by revenge."
The spur for the investigation is ostensibly to get to the bottom of the ethnic turmoil in June 2010 that left at least 446 people dead in the southern cities of Osh and Jalal-Abad. The State Committee for National Security, or GKNB, announced in April 2021 that it was initiating a fresh look at those events and implied that members of the 2010 interim government might face questions. Japarov had said earlier that same month that he wanted investigators "to provide a full account on decisions made then by state bodies."
The decision to reopen this painful chapter in the country's history has not been motivated by an attempt to redress wrongs. Although the bulk of those killed were ethnic Uzbeks, almost nobody has faced prosecution over those deaths. The Kyrgyz government has also provided no compensation for the hundreds of Uzbek homes destroyed during what amounted to pogroms.
The GKNB has instead chosen to focus on claims that the interim government allegedly offered its backing to Kadyrjan Batyrov, a prominent ethnic Uzbek businessman regularly accused, without evidence, of promoting separatist sentiments among fellow Uzbeks. Their investigation lasted more than a year and more than 15 former and current officials were questioned. Among the people facing questions were Japarov himself and the current head of the GKNB, Kamchybek Tashiyev.
Tashiyev came out of his light-touch questioning session swinging at the interim government, claiming that they had supported local separatists and provoked inter-ethnic tensions in an attempt "to maintain their influence and power in the south."
Dushebayev has spoken publicly of his contempt for the accusations made against him and his colleagues.
"This case is a political hit. We are being pressured because we are in the opposition. There is no evidence. The investigation and trial must be fair, but we cannot count on it [fairness]," he said in an interview with RFE/RL's Kyrgyz service, Radio Azattyk. Isakov, who held the post of defence minister in 2010, likewise said the accusations were "without basis." Asanov, whose native Jalal-Abad region was also home to the Uzbek businessman Batyrov, has refrained from commenting publicly on the accusations.
Others may well be in the crosshairs. There has been speculation that the Prosecutor General intends to pursue the freezing of assets belonging to another six members of the interim government, including Roza Otunbayeva, who should enjoy immunity as the then-acting president. The Prosecutor General's Office has confirmed it has made formal enquiries about the holdings of nine members of the 2010 government, but officials deny any freeze is in motion.
One person who has had his property confiscated is Almazbek Atambayev, the imprisoned former president, who also worked his way to the top by means of a stint as prime minister in that interim government. On May 31, a representative for the State Property Management Fund announced that a country estate owned by Atambayev in a village outside Bishkek has been taken into state ownership and will be converted into a residential facility for the elderly.
Activists are bewildered by how the government has chosen to revisit the events of 2010 in this way. Aziza Abdyrasulova, a rights activist, noted that less than 2 percent of the more than 5,000 criminal cases opened after the ethnic unrest have been closed to satisfaction. The government would have been better placed expending its resources investigating cases of murder, rape and destruction of property, Abdyrasulova said.
Kyrgyzstan: Prosecutors use 2010 ethnic unrest as cudgel against government opponents. (2022). Intellinews. https://www.intellinews.com/kyrgyzstan-prosecutors-use-2010-ethnic-unrest-as-cudgel-against-government-opponents-246801/
abuse cudgel ethnic GKNB government kidnapping Kyrgyzstan opponents prison Prosecutor General Prosecutors sincere unrest witch-hunts


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Hippocrene Books. 186 pages. Includes 2,200 entries. No visit to the Philippines can be as rewarding as one in which the visitor has experienced firsthand the warm hospitality of one of Asia's most enchanting countries. Filipino (Tagalog), the national language of the Philippines, is the most widely understood of the eight main Philippine languages, with over 10 million speakers. The ability to speak just a few words and phrases will greatly enhance the experience of the beautiful Philippine islands. A two-way dictionary and a phrasebook, with topics ranging from accommodations to colloquial expressions, are complemented by basic grammar instruction as well as cultural information. Combining the benefits of both a dictionary and a phrasebook, this pocket-size volume provides the traveler or student with the basis for simple conversation. Over 2,500 dictionary entries. Pronunciation guide. Basic grammar. Essential phrases. Ideal for the traveler or student.
Filipino Word Book and Audio CD.
Bess Press. 128 pages. Illustrations. The book features 200-400 illustrated introductory vocabulary words, a pronunciation guide, and glossaries. The categories which include family, home, school, the body, clothing, food, opposites, numbers, nature, and time, accurately portray the Pinoy culture as well as teach basic vocabulary. An audio CD recorded by a native speaker is included. Recommended for ages 4-8, but adults will also find it invaluable as a first language primer. Captioned in Filipino, Ilocano, and English.
Filipino Language, "Head Start", Audio Cassette Course.
Foreign Service Institute (FSI). Includes 13 audio cassette tapes, plus a textbook. This is the best course for learning to speak Filipino quickly. Conversation, dialogues and practical vocabulary are the focus of this course. The illustrated book includes course materials and a cultural guide. Each unit of the 13 audio cassette tapes has different activities, including conversation and notes, exercises, and a self-evaluation quiz. Unit by unit objectives for each module are stated at the start of the module, and each module has a vocabulary at the end. This course was developed by the Defense Language Institute for use in its own renowned language school.
Filipino Language, "Head Start", Audio CD Course.
Foreign Service Institute (FSI). Includes 13 audio CD discs, plus a textbook. This is the best course for learning to speak Filipino quickly. Conversation, dialogues and practical vocabulary are the focus of this course. The illustrated book includes course materials and a cultural guide. Each unit of the 13 audio CD discs has different activities, including conversation and notes, exercises, and a self-evaluation quiz. Unit by unit objectives for each module are stated at the start of the module, and each module has a vocabulary at the end. This course was developed by the Defense Language Institute for use in its own renowned language school.
Includes two Audio Cassette tapes (approximately 100 minutes) and a verbatim phrase book. You can learn anytime, anywhere...in your car...while exercising...whenever! Easy to use. First the English phrase is spoken on the tape; then the Filipino language phrase is spoken twice for maximum learning; followed by a pause for student response. Includes basic Filipino language conversational phrases such as: greetings, personal needs, transportation, business, health and emergency terms, and more. Features native Filipino language voices with authentic pronunciation; phrases in both English and the Filipino language, with target phrases spoken twice for maximum learning; basic grammar section, pronunciation hints, updated social customs, vocabulary index, phonetic pronunciation, and foreign scripts. The Filipino language phrase book can be used separately as a handy, pocket-size reference guide, or used with the tape. Recommended for beginners, business travellers, vacationers, or as a refresher course.
Audio CD. Includes two audio CD discs tapes (approximately 100 minutes) and a verbatim phrase book. You can learn anytime, anywhere...in your car...while exercising...whenever! Easy to use. First the English phrase is spoken on the tape; then the Filipino language phrase is spoken twice for maximum learning; followed by a pause for student response. Includes basic Filipino language conversational phrases such as: greetings, personal needs, transportation, business, health and emergency terms, and more. Features native Filipino language voices with authentic pronunciation; phrases in both English and the Filipino language, with target phrases spoken twice for maximum learning; basic grammar section, pronunciation hints, updated social customs, vocabulary index, phonetic pronunciation, and foreign scripts. The Filipino language phrase book can be used separately as a handy, pocket-size reference guide, or used with the tape. Recommended for beginners, business travellers, vacationers, or as a refresher course.
Teach Yourself Filipino Language Course.
Audio CD Pack and Book. 352 pages. Size 5"x7?". Includes two 60-minute audio CD discs. This complete course is based on the very latest learning methods and is designed to be both enjoyable and user-friendly. Prepared by experts in the language, this course begins with the basics and gradually elevates the student to a level of smooth and confident communication. Includes up-to-date interactive dialogues; graded units of cultural notes, grammar, and exercises; practical vocabulary; step-by-step guides to pronunciation; irregular verb tables; and plenty of practice exercises. This is another good beginner language course and includes all the fundamentals of the language. This is a great way to learn and speak the Filipino language.
University of Hawaii Press. 330 pages. Contains 4,000 Filipino roots, affixes, stems, compounds, and idioms.


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Increasing GI Symptoms Seen in Approximately One-Third of Young Adults
Jessica Nye, PhD
Investigators sought to identify common GI symptoms in a large sample of "emerging adults" using the Patient-Reported Outcomes Measurement Information System – GI (PROMIS-GI) symptom scales.
Approximately one-third of young adults aged 18 to 25 years were found to experience at least 1 gastrointestinal (GI) symptom above normal levels. These survey findings, published in BMC Gastroenterology, suggest that mild to moderate GI symptoms indicative of bowel disorders appear to present at much younger ages and at a greater frequency than previously documented, the authors said.
The investigators recruited 956 students enrolled in introductory psychology courses at the University of Central Florida. Participants responded to a 198-question online survey, made available from May 2018 to December 2018, which included assessments from the Patient-Reported Outcomes Measurement Information System-GI (PROMIS-GI), Patient Health Questionnaire (PHQ-9), Generalized Anxiety Disorder Screener (GAD-7), Short Form Health Survey (SF-36), and Validity Check (VCheck).
The respondents' mean age was 19 years (standard deviation [SD], 1.5), 58.3% were women, 57.3% were White, and 65.8% had a body mass index between 18.5 and 24.9.
Approximately one-third (36.4%) of respondents experienced at least 1 GI symptom the week before the survey became available. The reported symptoms were gas or bloating (36.4%), nausea or vomiting (26.9%), belly pain (21.6%), constipation (11.7%), diarrhea (8.9%), and heartburn or reflux (6.8%).
The researchers found that the best fit model for the reported GI symptoms was a 3-class model that separated participants into normal (67.89%), mild (26.88%), and moderate (5.2%) groups. The principal differentiator among classes was symptom severity.
Individuals in the mild group were likely preclinical for a bowel disorder as they reported 3 symptoms with a 0.5-SD severity above the study population's mean score. Individuals in the moderate group were likely in the clinical range for a bowel disorder because they reported 4 symptoms with a 1.0-SD severity above the mean score.
The mild and moderate classes together reported the highest symptom elevations for gas or bloating, nausea or vomiting, and belly pain. These symptoms were generally consistent with an irritable bowel syndrome diagnosis (mixed or unclassified), but the rate of nausea or vomiting was higher than expected for a typical diagnosis.
Stratifying participants by their GI symptom classes, the investigators observed significant differences for their PHQ-9 scores (F, 47.924; h2, 0.092; P <.001), GAD-7 scores (F, 54.438; h2, 0.103; P <.001), and SF-36 scales for physical function (F, 5.013; h2, 0.010; P <.01), energy (F, 40.40; h2, 0.078; P <.001), emotional well-being (F, 42.205; h2, 0.081; P <.001), social function (F, 45.759; h2, 0.088; P <.001), pain (F, 66.402; h2, 0.122; P <.001), and general health (F, 42.971; h2, 0.083; P <.001).
The results from this study may not be generalizable to the general population because they were derived from a university setting, but the findings warrant further study of this population's GI health, the authors said.
"It is recommended that health service providers evaluate individual patterns of 'GI health' when young adults present with anxiety and depression, and conversely, they should assess anxiety and depression when they present with GI complains," they concluded.
Vivier H, Ross EJ, and Cassisi JE. Classification of gastrointestinal symptom patterns in young adults. BMC Gastroenterol. 2020;20(1):326. doi:10.1186/s12876-020-01478-7
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Rhino Factoids: S.P.O.T.S. (Sex Pistols On Tour Secretly)
70s Rhino Factoids
37 years ago today, the Sex Pistols embarked on a brief set of dates around the UK, but because of the amount of infamy they'd already accumulated during the course of their career, the band decided it'd be in their best interest to be booked at venues under fake names, resulting in what has come to be known as the S.P.O.T.S. tour, an acronym which stands for Sex Pistols On Tour Secretly.
In an interview included within Sex Pistols: The Inside Story, by Fred & Judy Vermorel, Paul Cook was asked to explain the thinking behind doing the secret gigs.
"Well, we decided to do these gigs, like, just for one, 'cause we want to play anyway, and we hadn't played in England for such a long time," said Cook. "And we couldn't publicize them, 'cause if we did, some councilor might just come and say, 'Right, you're not playing here,' we they have done and they can do, for any stupid reason. So we decided to go to each individual promoter ourselves, who owned their private clubs and who could put us on without having to ask someone else, and told them to keep it secret. But we knew enough word would get out that people would know we were playing – which they did. So it weren't totally unfair on the fans anyway, 'cause most of them who wanted to see us come to see us. And all the places were packed out, so enough word got 'round for people to know we were playing."
There was a minor freak-out when the plans for the secret gigs somehow made their way onto the front page of Melody Maker, but it turned out to be a tempest in a teacup, thankfully, as the magazine hadn't actually managed to get any of the dates or venues right. The Sex Pistols ultimately did six dates on the so-called S.P.O.T.S. tour, being billed differently in each of the half-dozen locations: Lafayette Club, Wolverhampton (S.P.O.T.S.); Outlook Club, Doncaster (Tax Exiles); Penthouse, Scarborough (Special Guest); Rock Garden, Middlesborough (Acne Rabble); Woods Centre, Plymouth (The Hamsters), and Winter Gardens, Penzance (A Mystery Band of International Repute). If nothing else, the brief jaunt helped get Sid Vicious out and about as the band's bassist, even if his limited playing ability proved evident.
Over at Vintagerock's Weblog, you can at least get a feel for what the Scarborough show was like. Here's an excerpt:
"The atmosphere was electric and the Pistols were incredible. Sid was new to the band, and was just learning to play bass, but he looked great; just the part. John was amazing, sneering and snarling, hanging off his mike stand and at times covered in spit from the crowd. Steve Jones was the ultimate rock guitar hero, all swagger in his leather jeans, and Paul Cook was smashing away at his drums. And they were loud, and fast. We braved it in the scrum down the front for some of the set, but I eventually bottled it and took up a vantage point at the back, standing on a chair. Too much spitting and pogoing down the front for my liking."
Amazingly, at this point the band's lone full-length studio offering, Never Mind the Bollocks, Here's the Sex Pistols, had yet to be released, but if you go over to read the rest of the write-up on the performance, it sounds like they played virtually all of it…and if you're anything like us, then you're suddenly finding yourself with a hankering to go listen to that album yourself, so allow us to provide you with the opportunity to do so.
Never Mind The Bollocks, Here's The Sex Pistols
More on Sex Pistols
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