Analogs of complementary series for CAT(-1) groups

Abstract

In this paper we extend the construction of complementary series representations to convex-cocompact isometry groups of CAT(-1) spaces with conditionally negative metrics. Our approach is purely dynamical and generalizes the constructions known for negatively curved algebraic groups as $SO(n,1)$, $SU(n,1)$ or $S{L}_2({\mathbb{Q}}_p)$ and their lattices to new examples as non-linear groups coming from lattices of certain hyperbolic buildings.

v2: minor modifications, minor improvement of Theorem 1