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arXiv · 2407.16317

Maximal subgroups of maximal rank in the classical algebraic groups

Vanthana Ganeshalingam·Damian Sercombe·Laura Voggesberger
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Abstract

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.

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Vanthana Ganeshalingam, Damian Sercombe, Laura Voggesberger. 2024-07-23. Maximal subgroups of maximal rank in the classical algebraic groups. https://arxiv.org/abs/2407.16317

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