Representations of twisted Yangians of types B, C, D: II
Nicolas Guay, Vidas Regelskis, Curtis Wendlandt
We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs $(\mathfrak{so}_N,\mathfrak{so}_{N-2} \oplus \mathfrak{so}_2)$ and $(\mathfrak{so}_{2n+1},\mathfrak{so}_{2n})$.
Transformation Groups
https://doi.org/10.1007/s00031-019-09514-x
E-pub ahead of print - 23 Feb 2019
© Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher's self-archiving policy. Further copying may not be permitted; contact the publisher for details.
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Guay, N., Regelskis, V., & Wendlandt, C. (2019). Representations of twisted Yangians of types B, C, D: II. Transformation Groups. https://doi.org/10.1007/s00031-019-09514-x
Guay, Nicolas ; Regelskis, Vidas ; Wendlandt, Curtis. / Representations of twisted Yangians of types B, C, D: II. In: Transformation Groups. 2019.
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title = "Representations of twisted Yangians of types B, C, D: II",
abstract = "We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs $(\mathfrak{so}_N,\mathfrak{so}_{N-2} \oplus \mathfrak{so}_2)$ and $(\mathfrak{so}_{2n+1},\mathfrak{so}_{2n})$.",
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author = "Nicolas Guay and Vidas Regelskis and Curtis Wendlandt",
note = "{\textcopyright} Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details.",
doi = "10.1007/s00031-019-09514-x",
journal = "Transformation Groups",
publisher = "Birkhause Boston",
Guay, N, Regelskis, V & Wendlandt, C 2019, 'Representations of twisted Yangians of types B, C, D: II', Transformation Groups. https://doi.org/10.1007/s00031-019-09514-x
Representations of twisted Yangians of types B, C, D: II. / Guay, Nicolas; Regelskis, Vidas; Wendlandt, Curtis.
In: Transformation Groups, 23.02.2019.
T1 - Representations of twisted Yangians of types B, C, D: II
AU - Guay, Nicolas
AU - Regelskis, Vidas
AU - Wendlandt, Curtis
N1 - © Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher's self-archiving policy. Further copying may not be permitted; contact the publisher for details.
N2 - We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs $(\mathfrak{so}_N,\mathfrak{so}_{N-2} \oplus \mathfrak{so}_2)$ and $(\mathfrak{so}_{2n+1},\mathfrak{so}_{2n})$.
AB - We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs $(\mathfrak{so}_N,\mathfrak{so}_{N-2} \oplus \mathfrak{so}_2)$ and $(\mathfrak{so}_{2n+1},\mathfrak{so}_{2n})$.
KW - math.RT
KW - math.QA
U2 - 10.1007/s00031-019-09514-x
DO - 10.1007/s00031-019-09514-x
JO - Transformation Groups
JF - Transformation Groups
Guay N, Regelskis V, Wendlandt C. Representations of twisted Yangians of types B, C, D: II. Transformation Groups. 2019 Feb 23. Epub 2019 Feb 23. doi: 10.1007/s00031-019-09514-x