Charmenability of arithmetic groups of product type

Uri Bader; Rémi Boutonnet; Cyril Houdayer; Jesse Peterson

doi:10.1007/s00222-022-01117-w

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arXiv · 2009.09952

Charmenability of arithmetic groups of product type

Uri Bader·Rémi Boutonnet·Cyril Houdayer·Jesse Peterson

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Abstract

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. We apply our discussion also to groups acting on product of trees.

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Uri Bader, Rémi Boutonnet, Cyril Houdayer, Jesse Peterson. 2020-09-21. Charmenability of arithmetic groups of product type. https://doi.org/10.1007/s00222-022-01117-w

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