Charmenability of arithmetic groups of product type

• 成果类型: Article
• 署名作者: Bader, Uri; Boutonnet, Remi; Houdayer, Cyril; Peterson, Jesse
• 署名单位: Weizmann Institute of Science; Universite de Bordeaux; Universite Paris Saclay; Vanderbilt University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01117-w
• 发表日期: 2022
• 页码: 929-985
• 关键词: lattices; RIGIDITY; THEOREM

摘要

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.