Generalization of the Macdonald formula for Hall-Littlewood polynomials

Details Generalization of the Macdonald formula for Hall-Littlewood polynomials Generalization of the Macdonald formula for Hall-Littlewood polynomials

2011-02-02

arxiv.org/abs/1102.0571v2

Mathematics

Combinatorics

Scientific paper

We study the Gaussent-Littelmann formula for Hall-Littlewood polynomials and we develop combinatorial tools to describe the formula in a purely combinatorial way for type A_n, B_n and C_n. This description is in terms of Young tableaux and arises from identifying one-skeleton galleries that appear in the Gaussent-Littelmann formula with Young tableaux. Furthermore, we show by using these tools that the Gaussent-Littelmann formula and the well-known Macdonald formula for Hall-Littlewood polynomials for type A_n are the same.

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