ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS
For a reductive group $G$ over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke category of the corresponding endoscopic group $H$ with trivial monodromy. We also extend this equivalen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2020-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508620000098/type/journal_article |
| _version_ | 1811156220201926656 |
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| author | GEORGE LUSZTIG ZHIWEI YUN |
| author_facet | GEORGE LUSZTIG ZHIWEI YUN |
| author_sort | GEORGE LUSZTIG |
| collection | DOAJ |
| description | For a reductive group $G$ over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke category of the corresponding endoscopic group $H$ with trivial monodromy. We also extend this equivalence to all blocks. We give two applications. One is a relationship between character sheaves on $G$ with a fixed semisimple parameter and unipotent character sheaves on the endoscopic group $H$, after passing to asymptotic versions. The other is a similar relationship between representations of $G(\mathbb{F}_{q})$ with a fixed semisimple parameter and unipotent representations of $H(\mathbb{F}_{q})$. |
| first_indexed | 2024-04-10T04:47:56Z |
| format | Article |
| id | doaj.art-1dcdaf052cfc4ca3b6d6e8be1ed60b9d |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:47:56Z |
| publishDate | 2020-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-1dcdaf052cfc4ca3b6d6e8be1ed60b9d2023-03-09T12:34:28ZengCambridge University PressForum of Mathematics, Pi2050-50862020-01-01810.1017/fmp.2020.9ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONSGEORGE LUSZTIG0ZHIWEI YUN1Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA;Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA;For a reductive group $G$ over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke category of the corresponding endoscopic group $H$ with trivial monodromy. We also extend this equivalence to all blocks. We give two applications. One is a relationship between character sheaves on $G$ with a fixed semisimple parameter and unipotent character sheaves on the endoscopic group $H$, after passing to asymptotic versions. The other is a similar relationship between representations of $G(\mathbb{F}_{q})$ with a fixed semisimple parameter and unipotent representations of $H(\mathbb{F}_{q})$.https://www.cambridge.org/core/product/identifier/S2050508620000098/type/journal_article20G4014F0514F4320C0820C33 |
| spellingShingle | GEORGE LUSZTIG ZHIWEI YUN ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS Forum of Mathematics, Pi 20G40 14F05 14F43 20C08 20C33 |
| title | ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS |
| title_full | ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS |
| title_fullStr | ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS |
| title_full_unstemmed | ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS |
| title_short | ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS |
| title_sort | endoscopy for hecke categories character sheaves and representations |
| topic | 20G40 14F05 14F43 20C08 20C33 |
| url | https://www.cambridge.org/core/product/identifier/S2050508620000098/type/journal_article |
| work_keys_str_mv | AT georgelusztig endoscopyforheckecategoriescharactersheavesandrepresentations AT zhiweiyun endoscopyforheckecategoriescharactersheavesandrepresentations |