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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.16317 |
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| _version_ | 1866914316282757120 |
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| author | Ganeshalingam, Vanthana Sercombe, Damian Voggesberger, Laura |
| author_facet | Ganeshalingam, Vanthana Sercombe, Damian Voggesberger, Laura |
| contents | Let $k$ be an arbitrary field. We classify the maximal reductive subgroups of maximal rank in any classical simple algebraic $k$-group in terms of combinatorial data associated to their indices. This result complements [S, 2022], which does the same for the exceptional groups. We determine which of these subgroups may be realised over a finite field, the real numbers, or over a $\mathfrak{p}$-adic field. We also look at the asymptotics of the number of such subgroups as the rank grows large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16317 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal subgroups of maximal rank in the classical algebraic groups Ganeshalingam, Vanthana Sercombe, Damian Voggesberger, Laura Group Theory 20G15, 20G07 Let $k$ be an arbitrary field. We classify the maximal reductive subgroups of maximal rank in any classical simple algebraic $k$-group in terms of combinatorial data associated to their indices. This result complements [S, 2022], which does the same for the exceptional groups. We determine which of these subgroups may be realised over a finite field, the real numbers, or over a $\mathfrak{p}$-adic field. We also look at the asymptotics of the number of such subgroups as the rank grows large. |
| title | Maximal subgroups of maximal rank in the classical algebraic groups |
| topic | Group Theory 20G15, 20G07 |
| url | https://arxiv.org/abs/2407.16317 |