Orthogonal Determinants of $\mathrm{GL}_n(q)$
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915063758061568 |
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| author | Hoyer, Linda |
| author_facet | Hoyer, Linda |
| contents | Let $n$ be a positive integer and $q$ be a power of an odd prime. We provide explicit formulas for calculating the orthogonal determinants $\det(χ)$, where $χ\in \mathrm{Irr}(\mathrm{GL}_n(q))$ is an orthogonal character of even degree. Moreover, we show that $\det(χ)$ is "odd". This confirms a special case of a conjecture by Richard Parker. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal Determinants of $\mathrm{GL}_n(q)$ Hoyer, Linda Representation Theory Let $n$ be a positive integer and $q$ be a power of an odd prime. We provide explicit formulas for calculating the orthogonal determinants $\det(χ)$, where $χ\in \mathrm{Irr}(\mathrm{GL}_n(q))$ is an orthogonal character of even degree. Moreover, we show that $\det(χ)$ is "odd". This confirms a special case of a conjecture by Richard Parker. |
| title | Orthogonal Determinants of $\mathrm{GL}_n(q)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.10797 |