A categorical approach to the stable center conjecture
Let G be a connected reductive group over a local non-archimedean field F. The stable center conjecture provides an intrinsic decomposition of the set of equivalence classes of smooth irreducible representations of G(F), which is only slightly coarser than the conjectural decomposition into L-packet...
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| Format: | Article |
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Société mathématique de France
2018
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| Online Access: | http://hdl.handle.net/1721.1/116254 https://orcid.org/0000-0001-5902-8989 |
| _version_ | 1811097273462947840 |
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| author | Kazhdan, David Bezrukavnikov, Roman Varshavsky, Yaakov |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kazhdan, David Bezrukavnikov, Roman Varshavsky, Yaakov |
| author_sort | Kazhdan, David |
| collection | MIT |
| description | Let G be a connected reductive group over a local non-archimedean field F. The stable center conjecture provides an intrinsic decomposition of the set of equivalence classes of smooth irreducible representations of G(F), which is only slightly coarser than the conjectural decomposition into L-packets. In this work we propose a way to verify this conjecture for depth zero representations. As an illustration of our method, we show that the Bernstein projector to the depth zero spectrum is stable. |
| first_indexed | 2024-09-23T16:57:03Z |
| format | Article |
| id | mit-1721.1/116254 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:57:03Z |
| publishDate | 2018 |
| publisher | Société mathématique de France |
| record_format | dspace |
| spelling | mit-1721.1/1162542022-10-03T09:22:10Z A categorical approach to the stable center conjecture Kazhdan, David Bezrukavnikov, Roman Varshavsky, Yaakov Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman Varshavsky, Yaakov Let G be a connected reductive group over a local non-archimedean field F. The stable center conjecture provides an intrinsic decomposition of the set of equivalence classes of smooth irreducible representations of G(F), which is only slightly coarser than the conjectural decomposition into L-packets. In this work we propose a way to verify this conjecture for depth zero representations. As an illustration of our method, we show that the Bernstein projector to the depth zero spectrum is stable. United States-Israel Binational Science Foundation (Grant 2012365) National Science Foundation (U.S.) (Grant DMS-1102434) Israel Science Foundation (Grant 598/09) Israel Science Foundation (Grant 1017/13) 2018-06-12T15:11:29Z 2018-06-12T15:11:29Z 2015 2018-05-16T18:55:31Z Article http://purl.org/eprint/type/JournalArticle 0303-1179 http://hdl.handle.net/1721.1/116254 Bezrukavnikov, Roman, David Kazhdan, and Yakov Varshavsky. "A Categorial Approach to the Stable Center Conjecture." Astérisque, 369, 2015, pp. 27-97. https://orcid.org/0000-0001-5902-8989 http://smf4.emath.fr/en/Publications/Asterisque/2015/369/html/ Astérisque Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Société mathématique de France arXiv |
| spellingShingle | Kazhdan, David Bezrukavnikov, Roman Varshavsky, Yaakov A categorical approach to the stable center conjecture |
| title | A categorical approach to the stable center conjecture |
| title_full | A categorical approach to the stable center conjecture |
| title_fullStr | A categorical approach to the stable center conjecture |
| title_full_unstemmed | A categorical approach to the stable center conjecture |
| title_short | A categorical approach to the stable center conjecture |
| title_sort | categorical approach to the stable center conjecture |
| url | http://hdl.handle.net/1721.1/116254 https://orcid.org/0000-0001-5902-8989 |
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