Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Complementary series and Riesz operators for hyperbolic groups

Talk by Prof. Dr. Jean-Claude Picaud

**Date:** 30.05.22 **Time:** 14.05 - 15.05 **Room:** ETH HG G 43

We investigate the set of (equivalence classes) of representations π : Γ → B(H) where Γ is an hyperbolic group, non virtually abelian and B(H) is the space of bounded operators of a separable Hilbert space H. To each geometric action of Γ on a metric space (X, d) we associate a family (πt)t∈[0,1] of boundary representations, analog to complementary series for SL(2, R). We discuss their irreducibility as well as the role of Riesz operators as intertwinners between representations. We will make an effort for the part of the audience not familiar with representation theory of infinite discrete groups. Joint work with Adrien Boyer (Paris University).