The isomorphism type of the centralizer of an element in a Lie group

Abstract

Let G be an 1-connected simple Lie group, and let x\inG be a group element. We determine the isomorphism type of the centralizer C_{x} in term of a minimal geodesic joinning the group unit e\inG to x. This result is applied to classify the isomorphism types of maximal subgroups of maximal rank of G, and the isomorphism types of parabolic subgroups of G.

arXiv comment35 pages; 5 tables

Cited by in corpus (1)

• The isomorphism types of parabolic subgroups in Kac-Moody groups