Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groups
Algebraic Geometry
2020-05-19 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1904.08629,
title = {Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groups},
author = {Maarten Solleveld},
journal= {arXiv preprint arXiv:1904.08629},
year = {2020}
}