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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.05719 |
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| _version_ | 1866917662154555392 |
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| author | Dagar, Prem Verma, Mahendra Kumar |
| author_facet | Dagar, Prem Verma, Mahendra Kumar |
| contents | Let F be a non-Archimedean local field. Consider G_n:= GL_n(F) and let M:= G_l * G_{n-l} be a maximal Levi subgroup of G_n. In this article, we compute the semisimplified Jacquet module of representations of G_n with respect to the maximal Levi subgroup M, belonging to a particular category of representations. Utilizing our results, we prove that the Jacquet module is multiplicity-free for a specific subcategory of representations. Our findings are based on the Zelevinsky classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Jacquet modules of general linear groups Dagar, Prem Verma, Mahendra Kumar Representation Theory 20G05, 20C30, 20C33, 46F10, 47A67 Let F be a non-Archimedean local field. Consider G_n:= GL_n(F) and let M:= G_l * G_{n-l} be a maximal Levi subgroup of G_n. In this article, we compute the semisimplified Jacquet module of representations of G_n with respect to the maximal Levi subgroup M, belonging to a particular category of representations. Utilizing our results, we prove that the Jacquet module is multiplicity-free for a specific subcategory of representations. Our findings are based on the Zelevinsky classification. |
| title | A note on Jacquet modules of general linear groups |
| topic | Representation Theory 20G05, 20C30, 20C33, 46F10, 47A67 |
| url | https://arxiv.org/abs/2405.05719 |