Charmenability and stiffness of arithmetic groups

  • Uri Bader

    Weizmann Institute of Science, Rehovot, Israel
  • Itamar Vigdorovich

    Weizmann Institute of Science, Rehovot, Israel
Charmenability and stiffness of arithmetic groups cover
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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.

Cite this article

Uri Bader, Itamar Vigdorovich, Charmenability and stiffness of arithmetic groups. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1535