2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130794We 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.28 pages, v3: revised version, to appear in IMRNCombinatoricsRepresentation Theory05E05;33D52text