## Journal of Mathematics of Kyoto University

- J. Math. Kyoto Univ.
- Volume 47, Number 2 (2007), 269-320.

### Characters of wreath products of compact groups with the infinite symmetric group and characters of their canonical subgroups

Takeshi Hirai and Etsuko Hirai

#### Abstract

Characters of wreath products $G=\mathfrak{S}_{\infty}(T)$ of any compact groups $T$ with the infinite symmetric group $\mathfrak{S}_{\infty}$ are studied. It is proved that the set $E(G)$ of all normalized characters is equal to the set $F(G)$ of all normalized *factorizable* continuous positive definite class functions. A general explicit formula of $f_{A} \in E(G)$ is given corresponding to a parameter $A=\left( \left( \alpha_{\zeta ,\epsilon} \right)_{({\zeta ,\epsilon})\in \hat{T}\times\{0,1\}} ; \mu \right)$. Similar results are obtained for certain canonical subgroups of $G$.

#### Article information

**Source**

J. Math. Kyoto Univ., Volume 47, Number 2 (2007), 269-320.

**Dates**

First available in Project Euclid: 14 August 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.kjm/1250281047

**Digital Object Identifier**

doi:10.1215/kjm/1250281047

**Mathematical Reviews number (MathSciNet)**

MR2376958

**Zentralblatt MATH identifier**

1176.20010

**Subjects**

Primary: 20C32: Representations of infinite symmetric groups

Secondary: 22Cxx: Compact groups

#### Citation

Hirai, Takeshi; Hirai, Etsuko. Characters of wreath products of compact groups with the infinite symmetric group and characters of their canonical subgroups. J. Math. Kyoto Univ. 47 (2007), no. 2, 269--320. doi:10.1215/kjm/1250281047. https://projecteuclid.org/euclid.kjm/1250281047