Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra

Abstract

In this paper we provide a combinatorial description of the coefficients appearing in the expansion of Hall-Littlewood polynomials in terms of monomial symmetric polynomials. Using this we proof a combinatorial formula for the structure constants of the spherical Hecke algebra. We also give a geometric interpretation of these coefficients. 1