Restriction of a character sheaf to conjugacy classes
Let A be a character sheaf on a connected reductive group G over an algebraically closed field. Assuming that the characteristic is not bad we show that for certain conjugacy classes D in G, the restriction of A to D is a local system up to shift. We also give a parametrization of unipotent cuspidal...
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| Format: | Article |
| Language: | en_US |
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Societatea de Ştiinţe Matematice din România
2016
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| Online Access: | http://hdl.handle.net/1721.1/105143 https://orcid.org/0000-0001-9414-6892 |
| _version_ | 1826217358783414272 |
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| author | Lusztig, George |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, George |
| author_sort | Lusztig, George |
| collection | MIT |
| description | Let A be a character sheaf on a connected reductive group G over an algebraically closed field. Assuming that the characteristic is not bad we show that for certain conjugacy classes D in G, the restriction of A to D is a local system up to shift. We also give a parametrization of unipotent cuspidal character sheaves of G in terms of restriction to conjugacy classes. Without restriction on characteristic we define canonical bijections from the set of unipotent representations of the corresponding split group over a finite field to a set combinatorially defined in terms of the Weyl group. |
| first_indexed | 2024-09-23T17:02:24Z |
| format | Article |
| id | mit-1721.1/105143 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:02:24Z |
| publishDate | 2016 |
| publisher | Societatea de Ştiinţe Matematice din România |
| record_format | dspace |
| spelling | mit-1721.1/1051432022-10-03T09:59:22Z Restriction of a character sheaf to conjugacy classes Lusztig, George Massachusetts Institute of Technology. Department of Mathematics Lusztig, George Let A be a character sheaf on a connected reductive group G over an algebraically closed field. Assuming that the characteristic is not bad we show that for certain conjugacy classes D in G, the restriction of A to D is a local system up to shift. We also give a parametrization of unipotent cuspidal character sheaves of G in terms of restriction to conjugacy classes. Without restriction on characteristic we define canonical bijections from the set of unipotent representations of the corresponding split group over a finite field to a set combinatorially defined in terms of the Weyl group. National Science Foundation (U.S.) (Grant DMS-1303060) Simons Foundation 2016-10-28T19:08:41Z 2016-10-28T19:08:41Z 2015 Article http://purl.org/eprint/type/JournalArticle 2065-0264 1220-3874 http://hdl.handle.net/1721.1/105143 Lusztig, G. “Restriction of a character sheaf to conjugacy class.” Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie 106.3 (2015): 287–309. https://orcid.org/0000-0001-9414-6892 en_US http://ssmr.ro/bulletin/volumes/58-3/node8.html Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Societatea de Ştiinţe Matematice din România arXiv |
| spellingShingle | Lusztig, George Restriction of a character sheaf to conjugacy classes |
| title | Restriction of a character sheaf to conjugacy classes |
| title_full | Restriction of a character sheaf to conjugacy classes |
| title_fullStr | Restriction of a character sheaf to conjugacy classes |
| title_full_unstemmed | Restriction of a character sheaf to conjugacy classes |
| title_short | Restriction of a character sheaf to conjugacy classes |
| title_sort | restriction of a character sheaf to conjugacy classes |
| url | http://hdl.handle.net/1721.1/105143 https://orcid.org/0000-0001-9414-6892 |
| work_keys_str_mv | AT lusztiggeorge restrictionofacharactersheaftoconjugacyclasses |