The Plancherel formula for countable groups

نویسندگان

چکیده

We discuss a Plancherel formula for countable groups, which provides canonical decomposition of the regular representation such group Γ into direct integral factor representations. Our main result gives precise description this in terms FC-center Γfc (that is, normal subgroup consisting elements with finite conjugacy class); involves action an appropriate totally disconnected compact automorphisms Γfc. As application, we determine linear groups. In appendix, use to provide unified proof Thoma’s and Kaniuth’s theorems respectively characterize groups are type I those whose is II.

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ژورنال

عنوان ژورنال: Indagationes Mathematicae

سال: 2021

ISSN: ['0019-3577', '1872-6100']

DOI: https://doi.org/10.1016/j.indag.2021.01.002