Analogs of complementary series for CAT(-1) groups

2020/07/30 by Kévin Boucher, Boucher, Kevin
Mathematics · #20F67 22D10 37A46 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2007.15369

openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 SL₂(ℚ_p) and their lattices to new examples as non-linear groups coming from lattices of certain hyperbolic buildings.

Citations

• Random walks in negative curvature and boundary representations

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