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A combinatorial formula for Macdonald polynomials

By Arun Ram and Martha Yip

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 GLn. 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)

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.313.8931
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