The isomorphism type of the centralizer of an element in a Lie group (Q360156)

Let \(G\) be a simply connected compact simple Lie group. The authors determine for any \(x \in G\) the isomorphism type of the centralizer \(C_x\) in terms of a minimal geodesic joining the group unit \(e \in G\) and \(x\). The authors give an explicit procedure for calculating these \(C_x\). In the existing literature mainly methods of describing the local type of such centralizers may be found.NEWLINENEWLINEThis result, in particular, is applied to the classification of the isomorphism types of maximal subgroups of maximal rank in \(G\).NEWLINENEWLINEIn this paper, the authors consider only compact Lie groups, but sometimes they do not mentioned this condition explicitly.