Generalization of the Macdonald formula for Hall–Littlewood polynomials

Abstract

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 An, Bn and Cn. 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 An are the same up to an additional factorization.