English

Analogs of complementary series for CAT(-1) groups

Group Theory 2020-12-02 v2 Dynamical Systems Representation Theory

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)SO(n,1), SU(n,1)SU(n,1) or SL2(Qp)SL_2(\mathbb{Q}_p) and their lattices to new examples as non-linear groups coming from lattices of certain hyperbolic buildings.

Keywords

Cite

@article{arxiv.2007.15369,
  title  = {Analogs of complementary series for CAT(-1) groups},
  author = {Kevin Boucher},
  journal= {arXiv preprint arXiv:2007.15369},
  year   = {2020}
}

Comments

v2: minor modifications, minor improvement of Theorem 1

R2 v1 2026-06-23T17:31:28.445Z