2000 character limit reached
Analogs of complementary series for CAT(-1) groups (2007.15369v2)
Published 30 Jul 2020 in math.GR, math.DS, and math.RT
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 $SL_2(\mathbb{Q}_p)$ and their lattices to new examples as non-linear groups coming from lattices of certain hyperbolic buildings.