English

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}
}