Rémi Boutonnet: On the unitary dual of higher rank semi-simple lattices

Abstract

In this talk, based on joint work with Cyril Houdayer, I will present a curious property of the unitary representations of lattices in semi-simple higher rank Lie groups: either they contain a finite dimensional invariant subspace or they are factorizations of the regular representation, in a strong sense. I will explain how this result generalizes and unifies recent advances in operator algebras. Our approach relies on ergodic theory and stationary dynamical systems.