## Annals of Functional Analysis

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

### Unitary representations of infinite wreath products

Robert P. Boyer and Yun S. Yoo

#### Abstract

Using ${C}^{\ast}$-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

**Source**

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

**Dates**

Received: 19 September 2017

Accepted: 9 May 2018

First available in Project Euclid: 16 January 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1547629226

**Digital Object Identifier**

doi:10.1215/20088752-2018-0011

**Mathematical Reviews number (MathSciNet)**

MR3899959

**Zentralblatt MATH identifier**

07045488

**Subjects**

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

**Keywords**

wreath product Littlewood–Richardson rule group algebra primitive ideal postliminary

#### Citation

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. https://projecteuclid.org/euclid.afa/1547629226