On the depth r Bernstein projector
In this paper we prove an explicit formula for the Bernstein projector to representations of depth ≤ r. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representati...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer International Publishing
2019
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| Online Access: | http://hdl.handle.net/1721.1/120924 https://orcid.org/0000-0001-5902-8989 |
| _version_ | 1811093402620526592 |
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| author | Bezrukavnikov, Roman Kazhdan, David Varshavsky, Yakov |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman Kazhdan, David Varshavsky, Yakov |
| author_sort | Bezrukavnikov, Roman |
| collection | MIT |
| description | In this paper we prove an explicit formula for the Bernstein projector to representations of depth ≤ r. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representation. As another application, we deduce that the depth r Bernstein projector is stable. Moreover, for integral depths our proof is purely local. |
| first_indexed | 2024-09-23T15:44:23Z |
| format | Article |
| id | mit-1721.1/120924 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:44:23Z |
| publishDate | 2019 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1209242022-09-22T10:47:17Z On the depth r Bernstein projector Bezrukavnikov, Roman Kazhdan, David Varshavsky, Yakov Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman In this paper we prove an explicit formula for the Bernstein projector to representations of depth ≤ r. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representation. As another application, we deduce that the depth r Bernstein projector is stable. Moreover, for integral depths our proof is purely local. United States-Israel Binational Science Foundation (Grant 2012365) 2019-03-12T14:44:32Z 2019-03-12T14:44:32Z 2016-10 2019-03-12T05:14:02Z Article http://purl.org/eprint/type/JournalArticle 1022-1824 1420-9020 http://hdl.handle.net/1721.1/120924 Bezrukavnikov, Roman, David Kazhdan, and Yakov Varshavsky. “On the Depth r Bernstein Projector.” Selecta Mathematica 22, no. 4 (October 2016): 2271–2311. https://orcid.org/0000-0001-5902-8989 en https://doi.org/10.1007/s00029-016-0278-2 Selecta Mathematica Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer International Publishing application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Bezrukavnikov, Roman Kazhdan, David Varshavsky, Yakov On the depth r Bernstein projector |
| title | On the depth r Bernstein projector |
| title_full | On the depth r Bernstein projector |
| title_fullStr | On the depth r Bernstein projector |
| title_full_unstemmed | On the depth r Bernstein projector |
| title_short | On the depth r Bernstein projector |
| title_sort | on the depth r bernstein projector |
| url | http://hdl.handle.net/1721.1/120924 https://orcid.org/0000-0001-5902-8989 |
| work_keys_str_mv | AT bezrukavnikovroman onthedepthrbernsteinprojector AT kazhdandavid onthedepthrbernsteinprojector AT varshavskyyakov onthedepthrbernsteinprojector |