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

摘要

Starting from Jacobi-Trudi type determinantal 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(/t) 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 (c) 2005 Elsevier Inc. All rights reserved.