Commuting isometries of the complex hyperbolic space

Abstract

Let H C n H_{\mathbb {C}}^n denote the complex hyperbolic space of dimension n n . The group U ( n , 1 ) U(n,1) acts as the group of isometries of H C n H_{\mathbb {C}}^n . In this paper we investigate when two isometries of the complex hyperbolic space commute. Along the way we determine the centralizers.