Conjugation Orbits of Loxodromic Pairs in $SU(n,1)$

Abstract: 

Let SU(n,1)SU(n,1) be the isometry group of the nn-dimensional complex hyperbolic space. An element gg in SU(n,1)SU(n,1) is called loxodromic or hyperbolic if it has exactly two fixed points on the boundary of the complex hyperbolic space.  We shall discuss a classification of pairs of loxodromic elements in SU(n,1)SU(n,1) up to conjugacy. This talk is based on my joint work with Shiv Parsad.