Annals of Functional Analysis

Unitary representations of infinite wreath products

Robert P. Boyer and Yun S. Yoo

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Using C-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.

Article information

Ann. Funct. Anal., Volume 10, Number 1 (2019), 97-105.

Received: 19 September 2017
Accepted: 9 May 2018
First available in Project Euclid: 16 January 2019

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Zentralblatt MATH identifier

Primary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Secondary: 20C32: Representations of infinite symmetric groups 20C99: None of the above, but in this section 43A40: Character groups and dual objects 46L05: General theory of $C^*$-algebras

wreath product Littlewood–Richardson rule group algebra primitive ideal postliminary


Boyer, Robert P.; Yoo, Yun S. Unitary representations of infinite wreath products. Ann. Funct. Anal. 10 (2019), no. 1, 97--105. doi:10.1215/20088752-2018-0011.

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