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Article Dans Une Revue Algebraic Combinatorics Année : 2019

Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties

Quelques identités combinatoires apparaissant dans le calcul de la cohomologie des variétés de Shimura

Résumé

In the computation of the intersection cohomology of Shimura varieties, or of the L 2 cohomology of equal rank locally symmetric spaces, combinatorial identities involving averaged discrete series characters of real reductive groups play a large technical role. These identities can become very complicated and are not always well-understood (see for example the appendix of [8]). We propose a geometric approach to these identities in the case of Siegel modular varieties using the combinatorial properties of the Coxeter complex of the symmetric group. Apart from some introductory remarks about the origin of the identities, our paper is entirely combinatorial and does not require any knowledge of Shimura varieties or of representation theory.
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hal-03058366 , version 1 (11-12-2020)

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  • HAL Id : hal-03058366 , version 1

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Richard Ehrenborg, Sophie Morel, Margaret Readdy. Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties. Algebraic Combinatorics, 2019. ⟨hal-03058366⟩
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