Charmenability of arithmetic groups of product type

  title={Charmenability of arithmetic groups of product type},
  author={Uri Bader and R'emi Boutonnet and Cyril Houdayer and Jesse Peterson},
  journal={Inventiones mathematicae},
  pages={929 - 985}
We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability and charfiniteness and study their applications to the topological dynamics, ergodic theory and unitary representation theory of the given groups. To do that, we study singularity properties of equivariant normal ucp maps between certain von Neumann algebras… 
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