3 0 Ju l 2 00 4 A duality between q - multiplicities in tensor products and q - multiplicities of weights for the root systems B , C or
نویسنده
چکیده
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.
منابع مشابه
2 00 4 Branching rules , Kostka - Foulkes polynomials and q - multiplicities in tensor product for the root systems
The Kostka-Foulkes polynomials K λ,μ(q) related to a root system φ can be defined as alternated sums running over the Weyl group associated to φ. By restricting these sums over the elements of the symmetric group when φ is of type Bn, Cn orDn, we obtain again a class K̃ φ λ,μ(q) of Kostka-Foulkes polynomials. When φ is of type Cn or Dn there exists a duality beetween these polynomials and some n...
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The Kostka-Foulkes polynomials K λ,μ(q) related to a root system φ can be defined as alternated sums running over the Weyl group associated to φ. By restricting these sums over the elements of the symmetric group when φ is of type Bn, Cn orDn, we obtain again a class K̃ φ λ,μ(q) of Kostka-Foulkes polynomials. When φ is of type Cn or Dn there exists a duality beetween these polynomials and some n...
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