# A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$

A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$ - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

Abstract : 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

Mots-clés : Théorie des représentations Quantification Combinatoire

Autor: Cédric Lecouvey -

Fuente: https://hal.archives-ouvertes.fr/

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