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Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields II
Authors:Tomohiro Uchiyama
Institution:1. Division of Mathematics, National Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwant.uchiyama2170@gmail.com
Abstract:Let k be a separably closed field. Let G be a reductive algebraic k-group. We study Serre’s notion of complete reducibility of subgroups of G over k. In particular, using the recently proved center conjecture of Tits, we show that the centralizer of a k-subgroup H of G is G-completely reducible over k if it is reductive and H is G-completely reducible over k. We show that a regular reductive k-subgroup of G is G-completely reducible over k. We present examples where the number of overgroups of irreducible subgroups and the number of G(k)-conjugacy classes of k-anisotropic unipotent elements are infinite.
Keywords:Algebraic groups  complete reducibility  pseudo-reductivity  spherical buildings
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