Endoscopy for metaplectic affine Hecke categories
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911070569889792 |
|---|---|
| author | Dhillon, Gurbir Li, Yau Wing Yun, Zhiwei Zhu, Xinwen |
| author_facet | Dhillon, Gurbir Li, Yau Wing Yun, Zhiwei Zhu, Xinwen |
| contents | For a possibly twisted loop group $LG$, and any character sheaf of its Iwahori subgroup, we identify the associated affine Hecke category with a combinatorial category of Soergel bimodules. In fact, we prove such results for affine Hecke categories arising from central extensions of the loop group $LG$. Our results work for mod $\ell$ or integral $\ell$-adic coefficients.
As applications, we obtain endoscopic equivalences between affine Hecke categories, including the derived Satake equivalence for metaplectic groups, and a series of conjectures by Gaitsgory in quantum geometric Langlands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Endoscopy for metaplectic affine Hecke categories Dhillon, Gurbir Li, Yau Wing Yun, Zhiwei Zhu, Xinwen Representation Theory Algebraic Geometry 20G25, 20C08, 14F43 For a possibly twisted loop group $LG$, and any character sheaf of its Iwahori subgroup, we identify the associated affine Hecke category with a combinatorial category of Soergel bimodules. In fact, we prove such results for affine Hecke categories arising from central extensions of the loop group $LG$. Our results work for mod $\ell$ or integral $\ell$-adic coefficients. As applications, we obtain endoscopic equivalences between affine Hecke categories, including the derived Satake equivalence for metaplectic groups, and a series of conjectures by Gaitsgory in quantum geometric Langlands. |
| title | Endoscopy for metaplectic affine Hecke categories |
| topic | Representation Theory Algebraic Geometry 20G25, 20C08, 14F43 |
| url | https://arxiv.org/abs/2507.16667 |