2004/07/30 by Cédric Lecouvey, Cedric Lecouvey, Lecouvey, Cedric
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.math/0407522
arxiv created 2004/07/30 · openalex publication_date 2004/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from Jacobi-Trudi's type determinental expressions for the Schur functions corresponding to 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 derive formulas expressing the associated multiplicities in terms of Kostka numbers.