On Combinatorial Formulas for Macdonald Polynomials
Combinatorics
2008-05-01 v1 Representation Theory
Abstract
A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram-Yip formula compresses to a new formula, which is similar to the Haglund-Haiman-Loehr one but contains considerably fewer terms.
Cite
@article{arxiv.0804.4716,
title = {On Combinatorial Formulas for Macdonald Polynomials},
author = {Cristian Lenart},
journal= {arXiv preprint arXiv:0804.4716},
year = {2008}
}