Decomposed Levi subgroups in BD-covers of classical groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915521691123712 |
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| author | Li, Wen-Wei |
| author_facet | Li, Wen-Wei |
| contents | For finite topological central extensions of $p$-adic classical groups, Heiermann and Wu introduced the notion of decomposed Levi subgroups in their study of intertwining algebras. In this note, we show that for symplectic and special orthogonal groups over local fields, except the split $\mathrm{SO}(4)$, all Levi subgroups are decomposed if the central extension arises from the Brylinski-Deligne construction. Discussions for certain unitary groups, $\mathrm{SO}(4)$ and $\mathrm{GSpin}(2n+1)$ are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposed Levi subgroups in BD-covers of classical groups Li, Wen-Wei Representation Theory 22E50 (Primary) 11F70 (Secondary) For finite topological central extensions of $p$-adic classical groups, Heiermann and Wu introduced the notion of decomposed Levi subgroups in their study of intertwining algebras. In this note, we show that for symplectic and special orthogonal groups over local fields, except the split $\mathrm{SO}(4)$, all Levi subgroups are decomposed if the central extension arises from the Brylinski-Deligne construction. Discussions for certain unitary groups, $\mathrm{SO}(4)$ and $\mathrm{GSpin}(2n+1)$ are also given. |
| title | Decomposed Levi subgroups in BD-covers of classical groups |
| topic | Representation Theory 22E50 (Primary) 11F70 (Secondary) |
| url | https://arxiv.org/abs/2509.24571 |