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arXiv · 1004.0066

One-skeleton galleries, the path model and a generalization of Macdonald's formula for Hall-Littlewood polynomials

Stéphane Gaussent·Peter Littelmann
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Abstract

We give a direct geometric interpretation of the path model using galleries in the $1-$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 ${\tt A}_n$ turns out to be equivalent to Macdonald's formula.

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BibTeXRIS

Stéphane Gaussent, Peter Littelmann. 2010-04-01. One-skeleton galleries, the path model and a generalization of Macdonald's formula for Hall-Littlewood polynomials. https://arxiv.org/abs/1004.0066

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