Jordan decompositions of cocenters of reductive ����-adic groups
© 2019 American Mathematical Society. Cocenters of Hecke algebras H play an important role in studying mod ℓ or ℂ harmonic analysis on connected p-adic reductive groups. On the other hand, the depth r Hecke algebra Hr+ is well suited to study depth r smooth representations. In this paper, we study d...
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| Format: | Article |
| Language: | English |
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American Mathematical Society (AMS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135624 |
| _version_ | 1826217284844126208 |
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| author | He, Xuhua Kim, Ju-Lee |
| author_facet | He, Xuhua Kim, Ju-Lee |
| author_sort | He, Xuhua |
| collection | MIT |
| description | © 2019 American Mathematical Society. Cocenters of Hecke algebras H play an important role in studying mod ℓ or ℂ harmonic analysis on connected p-adic reductive groups. On the other hand, the depth r Hecke algebra Hr+ is well suited to study depth r smooth representations. In this paper, we study depth r rigid cocenters Hr+rig of a connected reductive p-adic group over rings of characteristic zero or ℓ ≠ p. More precisely, under some mild hypotheses, we establish a Jordan decomposition of the depth r rigid cocenter, hence find an explicit basis of Hr+rig. |
| first_indexed | 2024-09-23T17:00:59Z |
| format | Article |
| id | mit-1721.1/135624 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:00:59Z |
| publishDate | 2021 |
| publisher | American Mathematical Society (AMS) |
| record_format | dspace |
| spelling | mit-1721.1/1356242022-03-30T14:46:47Z Jordan decompositions of cocenters of reductive ����-adic groups He, Xuhua Kim, Ju-Lee © 2019 American Mathematical Society. Cocenters of Hecke algebras H play an important role in studying mod ℓ or ℂ harmonic analysis on connected p-adic reductive groups. On the other hand, the depth r Hecke algebra Hr+ is well suited to study depth r smooth representations. In this paper, we study depth r rigid cocenters Hr+rig of a connected reductive p-adic group over rings of characteristic zero or ℓ ≠ p. More precisely, under some mild hypotheses, we establish a Jordan decomposition of the depth r rigid cocenter, hence find an explicit basis of Hr+rig. 2021-10-27T20:24:19Z 2021-10-27T20:24:19Z 2019 2019-11-14T17:54:48Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135624 en 10.1090/ert/528 Representation Theory of the American Mathematical Society 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 (AMS) American Mathematical Society |
| spellingShingle | He, Xuhua Kim, Ju-Lee Jordan decompositions of cocenters of reductive ����-adic groups |
| title | Jordan decompositions of cocenters of reductive ����-adic groups |
| title_full | Jordan decompositions of cocenters of reductive ����-adic groups |
| title_fullStr | Jordan decompositions of cocenters of reductive ����-adic groups |
| title_full_unstemmed | Jordan decompositions of cocenters of reductive ����-adic groups |
| title_short | Jordan decompositions of cocenters of reductive ����-adic groups |
| title_sort | jordan decompositions of cocenters of reductive ���� adic groups |
| url | https://hdl.handle.net/1721.1/135624 |
| work_keys_str_mv | AT hexuhua jordandecompositionsofcocentersofreductiveadicgroups AT kimjulee jordandecompositionsofcocentersofreductiveadicgroups |