Deligne–Lusztig duality and wonderful compactification
Abstract We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne–Lusztig (or Alvis–Curtis) duality for p-adic groups and homological duality. This provides a new way to introduce an involution on the set of irreducible representations of...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/131387 |
| _version_ | 1826201356883460096 |
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| author | Bernstein, Joseph Bezrukavnikov, Roman Kazhdan, David |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bernstein, Joseph Bezrukavnikov, Roman Kazhdan, David |
| author_sort | Bernstein, Joseph |
| collection | MIT |
| description | Abstract
We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne–Lusztig (or Alvis–Curtis) duality for p-adic groups and homological duality. This provides a new way to introduce an involution on the set of irreducible representations of the group which has been defined by A. Zelevinsky for
$$G=GL(n)$$
G
=
G
L
(
n
)
and by A.-M. Aubert in general (less direct geometric approaches to this duality have been developed earlier by Schneider-Stuhler and by the second author). As a byproduct, we describe the Serre functor for representations of a p-adic group. |
| first_indexed | 2024-09-23T11:50:38Z |
| format | Article |
| id | mit-1721.1/131387 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:50:38Z |
| publishDate | 2021 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1313872023-02-17T17:01:09Z Deligne–Lusztig duality and wonderful compactification Bernstein, Joseph Bezrukavnikov, Roman Kazhdan, David Massachusetts Institute of Technology. Department of Mathematics Abstract We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne–Lusztig (or Alvis–Curtis) duality for p-adic groups and homological duality. This provides a new way to introduce an involution on the set of irreducible representations of the group which has been defined by A. Zelevinsky for $$G=GL(n)$$ G = G L ( n ) and by A.-M. Aubert in general (less direct geometric approaches to this duality have been developed earlier by Schneider-Stuhler and by the second author). As a byproduct, we describe the Serre functor for representations of a p-adic group. 2021-09-20T17:16:52Z 2021-09-20T17:16:52Z 2018-01-23 2020-09-24T21:10:27Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131387 en https://doi.org/10.1007/s00029-018-0391-5 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer International Publishing AG, part of Springer Nature application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Bernstein, Joseph Bezrukavnikov, Roman Kazhdan, David Deligne–Lusztig duality and wonderful compactification |
| title | Deligne–Lusztig duality and wonderful compactification |
| title_full | Deligne–Lusztig duality and wonderful compactification |
| title_fullStr | Deligne–Lusztig duality and wonderful compactification |
| title_full_unstemmed | Deligne–Lusztig duality and wonderful compactification |
| title_short | Deligne–Lusztig duality and wonderful compactification |
| title_sort | deligne lusztig duality and wonderful compactification |
| url | https://hdl.handle.net/1721.1/131387 |
| work_keys_str_mv | AT bernsteinjoseph delignelusztigdualityandwonderfulcompactification AT bezrukavnikovroman delignelusztigdualityandwonderfulcompactification AT kazhdandavid delignelusztigdualityandwonderfulcompactification |