A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$
Lecouvey, Cédric
HAL, hal-00003061 / Harvested from HAL
Text on HAL
Starting from Jacobi-Trudi's type determinental expressions for the Schur functions of types $B,C$ and $D,$ we define a natural $q$-analogue of the multiplicity $[V(\lambda):M(\mu)]$ when $M(\mu)$ is a tensor product of row or column shaped modules defined by $\mu$. We prove that these $q$-multiplicities are equal to certain Kostka-Foulkes polynomials related to the root systems $C$ or $D$.\ Finally we express the corresponding multiplicities in terms of Kostka numbers
Publié le : 2004-10-12
Classification:  Théorie des représentations,  Quantification,  Combinatoire,  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] 
@article{hal-00003061,
     author = {Lecouvey, C\'edric},
     title = {A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003061}
}

Lecouvey, Cédric. A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003061/