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

Christoph Schwer

Published 2005-06-15, updated 2006-10-10Version 3

We provide a combinatorial description of the coefficients appearing in the expansion of Hall-Littlewood polynomials in terms of monomial symmetric functions. We also give a Littlewood-Richardson rule for Hall-Littlewood polynomials. For proving this we use galleries to calculate Satake coefficients and structure constants of spherical Hecke algebras with arbitrary parameters.