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Generalization of the Macdonald formula for Hall-Littlewood polynomials

Algebra & Discrete Mathematics

Speaker: Inka Klostermann, Mathematisches Institut, Universität zu Köln
Location: 1147 MSB
Start time: Thu, Feb 9 2012, 3:10PM

Gaussent and Littelmann developed a formula for Hall-Littlewood polynomials in terms of one-skeleton galleries in the affine building. In type $A_n$, $B_n$ and $C_n$ these galleries can be described by using certain Young tableaux. In this talk I will explain how to translate the Gaussent-Littelmann formula into an easy purely combinatorial formula in terms of Young tableaux. It turns out that the resulting so-called combinatorial Gaussent-Littelmann formula coincides with the well-known Macdonald formula for Hall-Littlewood polynomials in type $A_n$.