One-skeleton galleries, Hall-Littlewood polynomials and the path model
Résumé
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.
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