Symplectic model for Zelevinsky modules of GL(n,D)
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908855800168448 |
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| author | Sharma, Hariom |
| author_facet | Sharma, Hariom |
| contents | Let D be a quaternion division algebra over a non-archimedean local field F of characteristic zero. This article demonstrates the existence and uniqueness of the symplectic model for a family of Zelevinsky modules of GL(n, D) to a family of irreducible representations of GL(n, D). For this family of irreducible representations, we identify a necessary condition under which a symplectic model can exist. This work extends a result of Offen and Sayag beyond the case D = F. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23917 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symplectic model for Zelevinsky modules of GL(n,D) Sharma, Hariom Representation Theory 22E50, 22E35, 11F70 Let D be a quaternion division algebra over a non-archimedean local field F of characteristic zero. This article demonstrates the existence and uniqueness of the symplectic model for a family of Zelevinsky modules of GL(n, D) to a family of irreducible representations of GL(n, D). For this family of irreducible representations, we identify a necessary condition under which a symplectic model can exist. This work extends a result of Offen and Sayag beyond the case D = F. |
| title | Symplectic model for Zelevinsky modules of GL(n,D) |
| topic | Representation Theory 22E50, 22E35, 11F70 |
| url | https://arxiv.org/abs/2602.23917 |