Charmenability and stiffness of arithmetic groups
Year: 2024
Type: article
Abstract: We characterize charmenability among arithmetic groups and deduce dichotomy statements pertaining to normal subgroups, characters, dynamics, representations and associated operator algebras. We do this by studying the stationary dynamics on the space of characters of the amenable radical, and in particular we establish stiffness: any stationary probability measure is invariant. This generalizes a classical result of Furstenberg for dynamics on the torus. Under a higher rank assumption, we show that any action on the space of characters of a finitely generated virtually nilpotent group is stiff.
DOI: 10.4171/jems/1535
Authors: Uri Bader, Itamar Vigdorovich
Institution: Weizmann Institute of Science
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402368106