A combinatorial formula for Macdonald polynomials
Combinatorics
2008-03-10 v1 Representation Theory
Abstract
In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals of type GL(n). At q=0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove walks and at q=t=0 these formulas specialize to the formula for the Weyl character in terms of the Littelmann path model (in the positively folded gallery form of Gaussent-Littelmann).
Cite
@article{arxiv.0803.1146,
title = {A combinatorial formula for Macdonald polynomials},
author = {Arun Ram and Martha Yip},
journal= {arXiv preprint arXiv:0803.1146},
year = {2008}
}