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

Abstract

AbstractStarting 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(λ):M(μ)] when M(μ) is a tensor product of row or column shaped modules defined by μ. 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 number

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