The isomorphism type of the centralizer of an element in a Lie group
Group Theory
2012-12-21 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1201.3394,
title = {The isomorphism type of the centralizer of an element in a Lie group},
author = {Haibao Duan and Shali Liu},
journal= {arXiv preprint arXiv:1201.3394},
year = {2012}
}
Comments
35 pages; 5 tables