A duality between q-multiplicities in tensor products and q-multiplicities of weights for the root systems B,C or D
Copyright policy )A duality between q-multiplicities in tensor products and q-multiplicities of weights for the root systems B,C or D
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 $[V(��):M(��)]$ when $M(��)$ is a tensor product of row or column shaped modules defined by $��$. 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.
Théorie des représentations, Symmetric functions and generalizations, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), characters, Representation theory, representation theory, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Lusztig q-analogues, Quantification, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Combinatoire, Characters, q-multiplicities, Representation Theory (math.RT), Mathematics - Representation Theory, Lusztig \(q\)-analogues
Théorie des représentations, Symmetric functions and generalizations, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), characters, Representation theory, representation theory, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Lusztig q-analogues, Quantification, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Combinatoire, Characters, q-multiplicities, Representation Theory (math.RT), Mathematics - Representation Theory, Lusztig \(q\)-analogues
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