Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.15190 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916143017492480 |
|---|---|
| author | Boumasmoud, Reda Ganapathy, Radhika |
| author_facet | Boumasmoud, Reda Ganapathy, Radhika |
| contents | We describe the center of the Hecke algebra of a type attached to a Bernstein block under some hypothesis. When $\bf G$ is a connected reductive group over non-archimedean local field $F$ that splits over a tamely ramified extension of $F$ and the residue characteristic of $F$ does not divide the order of the absolute Weyl group of $\bf G$, the works of Kim-Yu and Fintzen associate a type to each Bernstein block and our hypothesis is satisfied for such types. We use our results to give a description of the Bernstein center of the Hecke algebra $\mathcal{H}({\bf G } (F),K)$ when $K$ belongs to a nice family of compact open subgroups of ${\bf G}(F)$ (which includes all the Moy-Prasad filtrations of an Iwahori subgroup) via the theory of types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15190 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The center of Hecke algebras of types Boumasmoud, Reda Ganapathy, Radhika Representation Theory We describe the center of the Hecke algebra of a type attached to a Bernstein block under some hypothesis. When $\bf G$ is a connected reductive group over non-archimedean local field $F$ that splits over a tamely ramified extension of $F$ and the residue characteristic of $F$ does not divide the order of the absolute Weyl group of $\bf G$, the works of Kim-Yu and Fintzen associate a type to each Bernstein block and our hypothesis is satisfied for such types. We use our results to give a description of the Bernstein center of the Hecke algebra $\mathcal{H}({\bf G } (F),K)$ when $K$ belongs to a nice family of compact open subgroups of ${\bf G}(F)$ (which includes all the Moy-Prasad filtrations of an Iwahori subgroup) via the theory of types. |
| title | The center of Hecke algebras of types |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2210.15190 |