Rook placements and coadjoint orbits for maximal unipotent subgroups of finite symplectic groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917276648734720 |
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| author | Venchakov, Mikhail |
| author_facet | Venchakov, Mikhail |
| contents | Let $U$ be a maximal unipotent subgroup in a symplectic group over a finite field of sufficiently large characteristic $p$. According to the Kirillov's orbit method, the coadjoint orbits of the group $U$ play the key role in the description of irreducible complex characters of $U$. Almost all important classes of orbits and characters studied to the moment can be uniformly described as the orbits and characters associated with so-called orthogonal rook placements. In the paper, we construct a semi-direct decomposition for the corresponding irreducible characters in the spirit of the Mackey little group method. As a corollary, we present an explicit formula for the character corresponding to an orbit of maximal possible dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14933 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rook placements and coadjoint orbits for maximal unipotent subgroups of finite symplectic groups Venchakov, Mikhail Representation Theory Group Theory 20C15, 17B08, 20D15 Let $U$ be a maximal unipotent subgroup in a symplectic group over a finite field of sufficiently large characteristic $p$. According to the Kirillov's orbit method, the coadjoint orbits of the group $U$ play the key role in the description of irreducible complex characters of $U$. Almost all important classes of orbits and characters studied to the moment can be uniformly described as the orbits and characters associated with so-called orthogonal rook placements. In the paper, we construct a semi-direct decomposition for the corresponding irreducible characters in the spirit of the Mackey little group method. As a corollary, we present an explicit formula for the character corresponding to an orbit of maximal possible dimension. |
| title | Rook placements and coadjoint orbits for maximal unipotent subgroups of finite symplectic groups |
| topic | Representation Theory Group Theory 20C15, 17B08, 20D15 |
| url | https://arxiv.org/abs/2602.14933 |