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no. 5
Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties
Ehrenborg, Richard1; Morel, Sophie2; Readdy, Margaret1
1 University of Kentucky Department of Mathematics Lexington, KY 40506, USA
2 Princeton University, Department of Mathematics, Princeton, NJ 08540, USA
Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 863-878.

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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DOI: 10.5802/alco.66
Classification: 14G35, 05E45, 14F43, 05A18, 06A07, 06A11, 52B22
Keywords: Averaged discrete series characters, permutahedron, intersection cohomology, ordered set partitions, shellability

Ehrenborg, Richard 1; Morel, Sophie 2; Readdy, Margaret 1

1 University of Kentucky Department of Mathematics Lexington, KY 40506, USA
2 Princeton University, Department of Mathematics, Princeton, NJ 08540, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Ehrenborg, Richard; Morel, Sophie; Readdy, Margaret. Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties. Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 863-878. doi : 10.5802/alco.66. https://alco.centre-mersenne.org/articles/10.5802/alco.66/

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