  The Kostka-Foulkes polynomials $K$ related to a root system $\phi $ can be
defined as alternated sums running over the Weyl group associated to $\phi .$
By restricting these sums over the elements of the symmetric group when $% \phi
$ is of type $B,C$ or $D$, we obtain again a class $\widetilde{K}$ of
Kostka-Foulkes polynomials. When $\phi $ is of type $C$ or $D$ there exists a
duality beetween these polynomials and some natural $q$-multiplicities $U$ in
tensor product \cite{lec}. In this paper we first establish identities for the
$\widetilde{K}$ which implies in particular that they can be decomposed as sums
of Kostka-Foulkes polynomials related to the root system of type $A$ with
nonnegative integer coefficients. Moreover these coefficients are branching
rule coefficients. This allows us to clarify the connection beetween the
$q$-multiplicities $U$ and the polynomials defined by Shimozono and Zabrocki in
\cite{SZ}. Finally we establish that the $q$-multiplicities $U$ defined for the
tensor powers of the vector representation coincide up to a power of $q$ with
the one dimension sum $X$ introduced in \cite{Ok} This shows that in this case
the one dimension sums $% X$ are affine Kazhdan-Lusztig polynomials.

Combinatorics