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arXiv · 1904.08629

Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groups

Maarten Solleveld
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Abstract

We investigate Levi subgroups of a connected reductive algebraic group G, over a ground field K. We parametrize their conjugacy classes in terms of sets of simple roots and we prove that two Levi K-subgroups of G are rationally conjugate if and only if they are geometrically conjugate. These results are generalized to arbitrary connected linear algebraic K-groups. In that setting the appropriate analogue of a Levi subgroup is derived from the notion of a pseudo-parabolic subgroup.

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Maarten Solleveld. 2019-04-18. Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groups. https://doi.org/10.1016/j.jpaa.2019.106254

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