Uniform cell decomposition with applications to Chevalley groups
We express integrals of definable functions over definable sets uniformly for non-Archimedean local fields, extending results of Pas. We apply this to Chevalley groups, in particular proving that zeta functions counting conjugacy classes in congruence quotients of such groups depend only on the size...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1797099480079663104 |
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| author | Berman, M Derakhshan, J Onn, U Paajanen, P |
| author_facet | Berman, M Derakhshan, J Onn, U Paajanen, P |
| author_sort | Berman, M |
| collection | OXFORD |
| description | We express integrals of definable functions over definable sets uniformly for non-Archimedean local fields, extending results of Pas. We apply this to Chevalley groups, in particular proving that zeta functions counting conjugacy classes in congruence quotients of such groups depend only on the size of the residue field, for sufficiently large residue characteristic. In particular, the number of conjugacy classes in a congruence quotient depends only on the size of the residue field. The same holds for zeta functions counting dimensions of Hecke modules of intertwining operators associated to induced representations of such quotients. |
| first_indexed | 2024-03-07T05:24:20Z |
| format | Journal article |
| id | oxford-uuid:e007b160-1f72-4993-abe7-0b26c606fed5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:24:20Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:e007b160-1f72-4993-abe7-0b26c606fed52022-03-27T09:43:52ZUniform cell decomposition with applications to Chevalley groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e007b160-1f72-4993-abe7-0b26c606fed5EnglishSymplectic Elements at Oxford2011Berman, MDerakhshan, JOnn, UPaajanen, PWe express integrals of definable functions over definable sets uniformly for non-Archimedean local fields, extending results of Pas. We apply this to Chevalley groups, in particular proving that zeta functions counting conjugacy classes in congruence quotients of such groups depend only on the size of the residue field, for sufficiently large residue characteristic. In particular, the number of conjugacy classes in a congruence quotient depends only on the size of the residue field. The same holds for zeta functions counting dimensions of Hecke modules of intertwining operators associated to induced representations of such quotients. |
| spellingShingle | Berman, M Derakhshan, J Onn, U Paajanen, P Uniform cell decomposition with applications to Chevalley groups |
| title | Uniform cell decomposition with applications to Chevalley groups |
| title_full | Uniform cell decomposition with applications to Chevalley groups |
| title_fullStr | Uniform cell decomposition with applications to Chevalley groups |
| title_full_unstemmed | Uniform cell decomposition with applications to Chevalley groups |
| title_short | Uniform cell decomposition with applications to Chevalley groups |
| title_sort | uniform cell decomposition with applications to chevalley groups |
| work_keys_str_mv | AT bermanm uniformcelldecompositionwithapplicationstochevalleygroups AT derakhshanj uniformcelldecompositionwithapplicationstochevalleygroups AT onnu uniformcelldecompositionwithapplicationstochevalleygroups AT paajanenp uniformcelldecompositionwithapplicationstochevalleygroups |