Asymptotic Hecke algebras and involutions
In [11], a Hecke algebra module structure on a vector space spanned by the involutions in a Weyl group was defined and studied. In this paper this study is continued by relating it to the asymptotic Hecke algebra introduced in [6]. In particular we define a module over the asymptotic Hecke algebra...
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| Format: | Article |
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American Mathematical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/115861 https://orcid.org/0000-0001-9414-6892 |
| _version_ | 1811072889720406016 |
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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 | In [11], a Hecke algebra module structure on a vector space spanned by
the involutions in a Weyl group was defined and studied. In this paper this study is continued by relating it to the asymptotic Hecke algebra introduced in [6]. In particular we define a module over the asymptotic Hecke algebra which is spanned by the involutions in the Weyl group. We present a conjecture relating this module to equivariant vector bundles with respect to a group action on a finite set. This gives an explanation (not a proof) of a result of Kottwitz [3] in the case of classical Weyl groups, see 2.5. We also present a conjecture which realizes the module in [11] terms of an ideal in the Hecke algebra generated by a single element, see 3.4. |
| first_indexed | 2024-09-23T09:19:38Z |
| format | Article |
| id | mit-1721.1/115861 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:19:38Z |
| publishDate | 2018 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/1158612022-10-25T05:05:03Z Asymptotic Hecke algebras and involutions Lusztig, George Massachusetts Institute of Technology. Department of Mathematics Lusztig, George In [11], a Hecke algebra module structure on a vector space spanned by the involutions in a Weyl group was defined and studied. In this paper this study is continued by relating it to the asymptotic Hecke algebra introduced in [6]. In particular we define a module over the asymptotic Hecke algebra which is spanned by the involutions in the Weyl group. We present a conjecture relating this module to equivariant vector bundles with respect to a group action on a finite set. This gives an explanation (not a proof) of a result of Kottwitz [3] in the case of classical Weyl groups, see 2.5. We also present a conjecture which realizes the module in [11] terms of an ideal in the Hecke algebra generated by a single element, see 3.4. National Science Foundation (U.S.) (Grant DMS-0758262) 2018-05-24T18:09:32Z 2018-05-24T18:09:32Z 2014 2018-05-24T17:57:29Z Article http://purl.org/eprint/type/JournalArticle 9780821891704 9781470415235 0271-4132 1098-3627 http://hdl.handle.net/1721.1/115861 Lusztig, G. “Asymptotic Hecke Algebras and Involutions.” Contemporary Mathematics (2014): 267–278 © 2014 American Mathematical Society https://orcid.org/0000-0001-9414-6892 http://dx.doi.org/10.1090/conm/610/12156 Perspectives in Representation Theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Mathematical Society American Mathematical Society |
| spellingShingle | Lusztig, George Asymptotic Hecke algebras and involutions |
| title | Asymptotic Hecke algebras and involutions |
| title_full | Asymptotic Hecke algebras and involutions |
| title_fullStr | Asymptotic Hecke algebras and involutions |
| title_full_unstemmed | Asymptotic Hecke algebras and involutions |
| title_short | Asymptotic Hecke algebras and involutions |
| title_sort | asymptotic hecke algebras and involutions |
| url | http://hdl.handle.net/1721.1/115861 https://orcid.org/0000-0001-9414-6892 |
| work_keys_str_mv | AT lusztiggeorge asymptoticheckealgebrasandinvolutions |