On the Steinberg character of a semisimple p-adic group
We show that the character of the Steinberg representation of a split semisimple p-adic group at a very regular element is given (up to sign) by a power of q, the number of elements in the residue field. We also show that (under an assumption on the characteristic) the character of an Iwahori-spheri...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Mathematical Sciences Publishers
2015
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| Online Access: | http://hdl.handle.net/1721.1/92975 https://orcid.org/0000-0002-9184-0114 https://orcid.org/0000-0001-9414-6892 |
| _version_ | 1826216771883892736 |
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| author | Lusztig, George Kim, Ju-Lee |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, George Kim, Ju-Lee |
| author_sort | Lusztig, George |
| collection | MIT |
| description | We show that the character of the Steinberg representation of a split semisimple p-adic group at a very regular element is given (up to sign) by a power of q, the number of elements in the residue field. We also show that (under an assumption on the characteristic) the character of an Iwahori-spherical representation at a split very regular element is given by a trace in the corresponding Hecke algebra module. |
| first_indexed | 2024-09-23T16:52:51Z |
| format | Article |
| id | mit-1721.1/92975 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:52:51Z |
| publishDate | 2015 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | mit-1721.1/929752022-09-29T22:08:11Z On the Steinberg character of a semisimple p-adic group Lusztig, George Kim, Ju-Lee Massachusetts Institute of Technology. Department of Mathematics Kim, Ju-Lee Lusztig, George We show that the character of the Steinberg representation of a split semisimple p-adic group at a very regular element is given (up to sign) by a power of q, the number of elements in the residue field. We also show that (under an assumption on the characteristic) the character of an Iwahori-spherical representation at a split very regular element is given by a trace in the corresponding Hecke algebra module. National Science Foundation (U.S.) 2015-01-20T15:43:51Z 2015-01-20T15:43:51Z 2013-08 2012-11 Article http://purl.org/eprint/type/JournalArticle 0030-8730 0030-8730 http://hdl.handle.net/1721.1/92975 Kim, Julee, and George Lusztig. “ On the Steinberg Character of a Semisimple p -Adic Group .” Pacific Journal of Mathematics 265, no. 2 (2013): 499–509. https://orcid.org/0000-0002-9184-0114 https://orcid.org/0000-0001-9414-6892 en_US http://dx.doi.org/10.2140/pjm.2013.265.499 Pacific Journal of Mathematics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Mathematical Sciences Publishers arXiv |
| spellingShingle | Lusztig, George Kim, Ju-Lee On the Steinberg character of a semisimple p-adic group |
| title | On the Steinberg character of a semisimple p-adic group |
| title_full | On the Steinberg character of a semisimple p-adic group |
| title_fullStr | On the Steinberg character of a semisimple p-adic group |
| title_full_unstemmed | On the Steinberg character of a semisimple p-adic group |
| title_short | On the Steinberg character of a semisimple p-adic group |
| title_sort | on the steinberg character of a semisimple p adic group |
| url | http://hdl.handle.net/1721.1/92975 https://orcid.org/0000-0002-9184-0114 https://orcid.org/0000-0001-9414-6892 |
| work_keys_str_mv | AT lusztiggeorge onthesteinbergcharacterofasemisimplepadicgroup AT kimjulee onthesteinbergcharacterofasemisimplepadicgroup |