Orthogonal irreducible representations of finite solvable groups in odd dimension
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914655078711296 |
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| author | Korhonen, Mikko |
| author_facet | Korhonen, Mikko |
| contents | We prove that if $G$ is a finite irreducible solvable subgroup of an orthogonal group $O(V,Q)$ with $\dim V$ odd, then $G$ preserves an orthogonal decomposition of $V$ into $1$-spaces. In particular $G$ is monomial. This generalizes a theorem of Rod Gow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15586 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orthogonal irreducible representations of finite solvable groups in odd dimension Korhonen, Mikko Group Theory Representation Theory 20H20, 20C99 We prove that if $G$ is a finite irreducible solvable subgroup of an orthogonal group $O(V,Q)$ with $\dim V$ odd, then $G$ preserves an orthogonal decomposition of $V$ into $1$-spaces. In particular $G$ is monomial. This generalizes a theorem of Rod Gow. |
| title | Orthogonal irreducible representations of finite solvable groups in odd dimension |
| topic | Group Theory Representation Theory 20H20, 20C99 |
| url | https://arxiv.org/abs/2309.15586 |