A combinatorial formula for Macdonald polynomials

Details A combinatorial formula for Macdonald polynomials A combinatorial formula for Macdonald polynomials

2008-03-05

arxiv.org/abs/0803.1146v1

Mathematics

Combinatorics

Scientific paper

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).

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