A combinatorial formula for Macdonald polynomials
Copyright policy )A combinatorial formula for Macdonald polynomials
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).
- UNIVERSITY OF WISCONSIN-MADISON United States
- University of Melbourne Australia
- University of Wisconsin–Madison United States
- University of Wisconsin–Oshkosh United States
- Department of Mathematics and Statistics University of Melbourne Australia
Mathematics(all), Symmetric functions and generalizations, Alcove walks, Path model, Symmetric functions, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Combinatorial formulas, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, symmetric functions, Combinatorics (math.CO), Representation Theory (math.RT), 05E05, 33D52, path model, Mathematics - Representation Theory, alcove walks, combinatorial formulas
Mathematics(all), Symmetric functions and generalizations, Alcove walks, Path model, Symmetric functions, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Combinatorial formulas, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, symmetric functions, Combinatorics (math.CO), Representation Theory (math.RT), 05E05, 33D52, path model, Mathematics - Representation Theory, alcove walks, combinatorial formulas
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