One-skeleton galleries, the path model and a generalization of Macdonald's formula for Hall-Littlewood polynomials
Representation Theory
2011-04-08 v2 Combinatorics
Abstract
We give a direct geometric interpretation of the path model using galleries in the skeleton of the Bruhat-Tits building associated to a semi-simple algebraic group. This interpretation allows us to compute the coefficients of the expansion of the Hall-Littlewood polynomials in the monomial basis. The formula we obtain is a "geometric compression" of the one proved by Schwer, its specialization to the case turns out to be equivalent to Macdonald's formula.
Keywords
Cite
@article{arxiv.1004.0066,
title = {One-skeleton galleries, the path model and a generalization of Macdonald's formula for Hall-Littlewood polynomials},
author = {Stéphane Gaussent and Peter Littelmann},
journal= {arXiv preprint arXiv:1004.0066},
year = {2011}
}
Comments
43 pages, 3 pictures, some improvements in the presentation, semistandard tableaux for type B and C defined