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.

Revised:

Accepted:

Published online:

DOI: 10.5802/alco.66

Keywords: Averaged discrete series characters, permutahedron, intersection cohomology, ordered set partitions, shellability

^{1}; Morel, Sophie

^{2}; Readdy, Margaret

^{1}

@article{ALCO_2019__2_5_863_0, author = {Ehrenborg, Richard and Morel, Sophie and Readdy, Margaret}, title = {Some combinatorial identities appearing in the calculation of the cohomology of {Siegel} modular varieties}, journal = {Algebraic Combinatorics}, pages = {863--878}, publisher = {MathOA foundation}, volume = {2}, number = {5}, year = {2019}, doi = {10.5802/alco.66}, mrnumber = {4023569}, zbl = {07115044}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.66/} }

TY - JOUR AU - Ehrenborg, Richard AU - Morel, Sophie AU - Readdy, Margaret TI - Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties JO - Algebraic Combinatorics PY - 2019 SP - 863 EP - 878 VL - 2 IS - 5 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.66/ DO - 10.5802/alco.66 LA - en ID - ALCO_2019__2_5_863_0 ER -

%0 Journal Article %A Ehrenborg, Richard %A Morel, Sophie %A Readdy, Margaret %T Some combinatorial identities appearing in the calculation of the cohomology of Siegel modular varieties %J Algebraic Combinatorics %D 2019 %P 863-878 %V 2 %N 5 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.66/ %R 10.5802/alco.66 %G en %F ALCO_2019__2_5_863_0

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. http://www.numdam.org/articles/10.5802/alco.66/

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