UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS
0.1. Let G be a simple adjoint algebraic group defined and split over the finite field F[subscript q]. Let K[subscript 0] = [bar over F][subscript q]((ǫ)), K =[bar over F][subscript q]((ǫ)). We are interested in the characters of the standard representations (in the sense of Langlands) of G(K[subsc...
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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/1721.1/116079 https://orcid.org/0000-0001-9414-6892 |
| _version_ | 1811096474060062720 |
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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 | 0.1. Let G be a simple adjoint algebraic group defined and split over the finite
field F[subscript q]. Let K[subscript 0] = [bar over F][subscript q]((ǫ)), K =[bar over F][subscript q]((ǫ)). We are interested in the characters of the standard representations (in the sense of Langlands) of G(K[subscript 0]) corresponding to the (irreducible) unipotent representations ([L6]) of G(K[subscript 0]), restricted to the set G(K[subscript 0])[subscript rsc] = G(K)[subscript rsc] ∩ G(K[subscript 0]) where G(K)[subscript rsc] is the intersection of the set G(K)[subcript rs] of regular semisimple elements in G(K) with the set G(K)[subscript c] of compact elements in G(K) (that is, elements which normalize some Iwahori subgroup of G(K)); we call these restrictions the unipotent characters of G(K[subscript 0]). We hope that the unipotent characters (or some small linear combination of them) have a geometric meaning in the same way as the characters of (irreducible) unipotent representations of G(F[subscript q]) can be expressed in terms of character sheaves on G. Thus we are seeking some geometric objects on G(K)[subscript c] on which the Frobenius map acts and from which the unipotent characters can be recovered. |
| first_indexed | 2024-09-23T16:44:15Z |
| format | Article |
| id | mit-1721.1/116079 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:44:15Z |
| publishDate | 2018 |
| publisher | Société mathématique de France |
| record_format | dspace |
| spelling | mit-1721.1/1160792022-09-29T21:08:07Z UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS Lusztig, George Massachusetts Institute of Technology. Department of Mathematics Lusztig, George 0.1. Let G be a simple adjoint algebraic group defined and split over the finite field F[subscript q]. Let K[subscript 0] = [bar over F][subscript q]((ǫ)), K =[bar over F][subscript q]((ǫ)). We are interested in the characters of the standard representations (in the sense of Langlands) of G(K[subscript 0]) corresponding to the (irreducible) unipotent representations ([L6]) of G(K[subscript 0]), restricted to the set G(K[subscript 0])[subscript rsc] = G(K)[subscript rsc] ∩ G(K[subscript 0]) where G(K)[subscript rsc] is the intersection of the set G(K)[subcript rs] of regular semisimple elements in G(K) with the set G(K)[subscript c] of compact elements in G(K) (that is, elements which normalize some Iwahori subgroup of G(K)); we call these restrictions the unipotent characters of G(K[subscript 0]). We hope that the unipotent characters (or some small linear combination of them) have a geometric meaning in the same way as the characters of (irreducible) unipotent representations of G(F[subscript q]) can be expressed in terms of character sheaves on G. Thus we are seeking some geometric objects on G(K)[subscript c] on which the Frobenius map acts and from which the unipotent characters can be recovered. National Science Foundation (U.S.) (Grant DMS-0758262) 2018-06-05T13:27:31Z 2018-06-05T13:27:31Z 2015 2018-05-24T17:52:33Z Article http://purl.org/eprint/type/JournalArticle 0303-1179 http://hdl.handle.net/1721.1/116079 Lusztig, Geoge. "Unipotent almost characters of simple p-adic groups." Astérisque, 370, 2015, pp. 243-267 https://orcid.org/0000-0001-9414-6892 http://smf4.emath.fr/en/Publications/Asterisque/2015/370/html/smf_ast_370_243-267.php Astérisque Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Société mathématique de France arXiv |
| spellingShingle | Lusztig, George UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS |
| title | UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS |
| title_full | UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS |
| title_fullStr | UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS |
| title_full_unstemmed | UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS |
| title_short | UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS |
| title_sort | unipotent almost characters of simple p adic groups |
| url | http://hdl.handle.net/1721.1/116079 https://orcid.org/0000-0001-9414-6892 |
| work_keys_str_mv | AT lusztiggeorge unipotentalmostcharactersofsimplepadicgroups |