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).
On Combinatorial Formulas for Macdonald Polynomials
Monk rules for type $GL_n$ Macdonald polynomials
From Macdonald Polynomials to a Charge Statistic beyond Type A
![QR code for arXiv:0803.1146 [math.CO]](http://oss.arxitics.com/images/favicon.svg)