Using -algebraic techniques and especially AF-algebras, we present a complete classification of the continuous unitary representations for a class of infinite wreath product groups. These nonlocally compact groups are realized by a topological completion of the semidirect product of the countably infinite symmetric group acting on the countable direct product of a finite Abelian group.
"Unitary representations of infinite wreath products." Ann. Funct. Anal. 10 (1) 97 - 105, February 2019. https://doi.org/10.1215/20088752-2018-0011