Abstract
In the computation of the intersection cohomology of Shimura varieties, or of the L2 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.
| Original language | English |
|---|---|
| Pages (from-to) | 863-878 |
| Number of pages | 16 |
| Journal | Algebraic Combinatorics |
| Volume | 2 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© The journal and the authors, 2019.
Funding
Keywords. Averaged discrete series characters, permutahedron, intersection cohomology, ordered set partitions, shellability. Acknowledgements. This work was partially supported by grants from the Simons Foundation (#429370 to Richard Ehrenborg and #422467 to Margaret Readdy). This work was also partially supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).
| Funders | Funder number |
|---|---|
| LABEX MILYON | ANR-10-LABX-0070, ANR-11-IDEX-0007 |
| Simons Foundation | 422467, 429370 |
| Agence Nationale de la Recherche | |
| Université de Lyon |
Keywords
- Averaged discrete series characters
- Intersection cohomology
- Ordered set partitions
- Permutahedron
- Shellability
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics