Endoscopy for affine Hecke categories
We show that the neutral block of the affine monodromic Hecke category for a reductive group is monoidally equivalent to the neutral block of the affine Hecke category for the endoscopic group. The semisimple complexes of both categories can be identified with the generalized Soergel bimodules via t...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/139019 |
| _version_ | 1826204838504955904 |
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| author | Li, Yau Wing |
| author2 | Yun, Zhiwei |
| author_facet | Yun, Zhiwei Li, Yau Wing |
| author_sort | Li, Yau Wing |
| collection | MIT |
| description | We show that the neutral block of the affine monodromic Hecke category for a reductive group is monoidally equivalent to the neutral block of the affine Hecke category for the endoscopic group. The semisimple complexes of both categories can be identified with the generalized Soergel bimodules via the Soergel functor. We extend this identification of semisimple complexes to the neutral blocks of the affine Hecke categories by the technical machinery developed by Bezrukavnikov and Yun. |
| first_indexed | 2024-09-23T13:02:11Z |
| format | Thesis |
| id | mit-1721.1/139019 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:02:11Z |
| publishDate | 2022 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1390192022-01-15T03:29:38Z Endoscopy for affine Hecke categories Li, Yau Wing Yun, Zhiwei Massachusetts Institute of Technology. Department of Mathematics We show that the neutral block of the affine monodromic Hecke category for a reductive group is monoidally equivalent to the neutral block of the affine Hecke category for the endoscopic group. The semisimple complexes of both categories can be identified with the generalized Soergel bimodules via the Soergel functor. We extend this identification of semisimple complexes to the neutral blocks of the affine Hecke categories by the technical machinery developed by Bezrukavnikov and Yun. Ph.D. 2022-01-14T14:45:00Z 2022-01-14T14:45:00Z 2021-06 2021-05-25T12:47:10.366Z Thesis https://hdl.handle.net/1721.1/139019 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Li, Yau Wing Endoscopy for affine Hecke categories |
| title | Endoscopy for affine Hecke categories |
| title_full | Endoscopy for affine Hecke categories |
| title_fullStr | Endoscopy for affine Hecke categories |
| title_full_unstemmed | Endoscopy for affine Hecke categories |
| title_short | Endoscopy for affine Hecke categories |
| title_sort | endoscopy for affine hecke categories |
| url | https://hdl.handle.net/1721.1/139019 |
| work_keys_str_mv | AT liyauwing endoscopyforaffineheckecategories |