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

Abstract

Let ${\mathbf{H}}_{\mathbb{C}}^n$ be the $n$-dimensional complex hyperbolic space and $\mathrm{SU}(n,1)$ be the (holomorphic) isometry group. An element $g$ in $\mathrm{SU}(n,1)$ is called loxodromic or hyperbolic if it has exactly two fixed points on the boundary $\partial {\mathbf{H}}_{\mathbb{C}}^n$. We classify $\mathrm{SU}(n,1)$ conjugation orbits of pairs of loxodromic elements in $\mathrm{SU}(n,1)$.

arXiv commentfinal version. to appear in Bull. Sci. Math