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

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

2005-06-15

arxiv.org/abs/math/0506287v3

IMRN, Volume 2006 (2006)

Mathematics

Combinatorics

28 pages, v3: revised version, to appear in IMRN

Scientific paper

10.1155/IMRN/2006/75395

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.

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