A combinatorial formula for Macdonald polynomials

Arun Ram; Martha Yip

doi:10.1016/j.aim.2010.06.022

A combinatorial formula for Macdonald polynomials

Arun Ram
, Martha Yip

Mathematics

Producción científica: Article › revisión exhaustiva

56 Citas (Scopus)

Resumen

In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials 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 and Littelmann).

Idioma original	English
Páginas (desde-hasta)	309-331
Número de páginas	23
Publicación	Advances in Mathematics
Volumen	226
N.º	1
DOI	https://doi.org/10.1016/j.aim.2010.06.022
Estado	Published - ene 15 2011

Nota bibliográfica

Funding Information:
This research was partially supported by the National Science Foundation (NSF) under grant DMS-0353038 at the University of Wisconsin, Madison. We thank the NSF for continuing support of our research. This paper was completed while the authors were in residence at the special semester in Combinatorial Representation Theory at Mathematical Sciences Research Institute (MSRI). It is a pleasure to thank MSRI for hospitality, support and a wonderful and stimulating working environment. A. Ram thanks S. Griffeth for many instructive conversations about double affine Hecke algebras and Macdonald polynomials.

Financiación

This research was partially supported by the National Science Foundation (NSF) under grant DMS-0353038 at the University of Wisconsin, Madison. We thank the NSF for continuing support of our research. This paper was completed while the authors were in residence at the special semester in Combinatorial Representation Theory at Mathematical Sciences Research Institute (MSRI). It is a pleasure to thank MSRI for hospitality, support and a wonderful and stimulating working environment. A. Ram thanks S. Griffeth for many instructive conversations about double affine Hecke algebras and Macdonald polynomials.

Financiadores	Número del financiador
National Science Foundation (NSF)	DMS-0353038
Directorate for Mathematical and Physical Sciences	0353038

ASJC Scopus subject areas

General Mathematics

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title = "A combinatorial formula for Macdonald polynomials",

abstract = "In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials 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 and Littelmann).",

keywords = "Alcove walks, Combinatorial formulas, Macdonald polynomials, Path model, Symmetric functions",

author = "Arun Ram and Martha Yip",

note = "Funding Information: This research was partially supported by the National Science Foundation (NSF) under grant DMS-0353038 at the University of Wisconsin, Madison. We thank the NSF for continuing support of our research. This paper was completed while the authors were in residence at the special semester in Combinatorial Representation Theory at Mathematical Sciences Research Institute (MSRI). It is a pleasure to thank MSRI for hospitality, support and a wonderful and stimulating working environment. A. Ram thanks S. Griffeth for many instructive conversations about double affine Hecke algebras and Macdonald polynomials.",

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N2 - In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials 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 and Littelmann).

AB - In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials 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 and Littelmann).

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KW - Path model

KW - Symmetric functions

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A combinatorial formula for Macdonald polynomials

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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