On combinatorial formulas for Macdonald polynomials

被引：9

作者：

Lenart, Cristian ^{[1
]}

机构：

[1] SUNY Albany, Dept Math & Stat, Albany, NY 12222 USA

来源：

ADVANCES IN MATHEMATICS | 2009年 / 220卷 / 01期

基金：

美国国家科学基金会;

关键词：

Macdonald polynomials; Alcove walks; Ram-Yip formula; Haglund-Haiman-Loehr formula; CRYSTALS; MODEL;

D O I：

10.1016/j.aim.2008.09.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：324 / 340

页数：17