Harish-Chandra Induction and Jordan Decomposition of Characters
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914546575212544 |
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| author | Arote, Prashant Mishra, Manish |
| author_facet | Arote, Prashant Mishra, Manish |
| contents | We show that for any finite connected reductive group, a Jordan decomposition can always be chosen such that it commutes with Harish-Chandra induction. En route, we show that the endomorphism algebra of the Harish-Chandra induction of a cuspidal representation of a Levi subgroup is isomorphic to a unipotent counterpart. These results generalize the well known results for groups with connected center. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00574 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Harish-Chandra Induction and Jordan Decomposition of Characters Arote, Prashant Mishra, Manish Representation Theory 20C33 We show that for any finite connected reductive group, a Jordan decomposition can always be chosen such that it commutes with Harish-Chandra induction. En route, we show that the endomorphism algebra of the Harish-Chandra induction of a cuspidal representation of a Levi subgroup is isomorphic to a unipotent counterpart. These results generalize the well known results for groups with connected center. |
| title | Harish-Chandra Induction and Jordan Decomposition of Characters |
| topic | Representation Theory 20C33 |
| url | https://arxiv.org/abs/2209.00574 |