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Main Authors: Ganeshalingam, Vanthana, Sercombe, Damian, Voggesberger, Laura
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.16317
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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