Stationary characters on lattices of semisimple Lie groups
Language
en
Article de revue
This item was published in
Publications mathematiques de l' IHES. 2021
English Abstract
We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications ...Read more >
We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation theory, operator algebras, ergodic theory and topological dynamics. In particular, we show that for any such irreducible lattice $\Gamma < G$, the left regular representation $\lambda_\Gamma$ is weakly contained in any weakly mixing representation $\pi$. We prove that for any such irreducible lattice $\Gamma < G$, any uniformly recurrent subgroup (URS) of $\Gamma$ is finite, answering a question of Glasner-Weiss. We also obtain a new proof of Peterson's character rigidity result for irreducible lattices $\Gamma < G$. The main novelty of our paper is a structure theorem for stationary actions of lattices on von Neumann algebras.Read less <
ANR Project
Algèbres d'Opérateurs et Dynamique des Groupes - ANR-19-CE40-0008
Origin
Hal imported