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2009 Limits of characters of wreath products ${\mathfrak S}_{n}(T)$ of a compact group $T$ with the symmetric groups and characters of ${\mathfrak S}_{\infty}(T)$, I
Takeshi Hirai, Etsuko Hirai, Akihito Hora
Nagoya Math. J. 193: 1-93 (2009).

Abstract

In the first half of this paper, all the limits of irreducible characters of $G_{n} = {\mathfrak S}_{n}(T)$ as $n \to \infty$ are calculated. The set of all \emph{continuous} limit functions on $G = {\mathfrak S}_{\infty}(T)$ is exactly equal to the set of all characters of $G$ determined in [HH6]. We give a necessary and sufficient condition for a series of irreducible characters of $G_{n}$ to have a continuous limit and also such a condition to have a discontinuous limit. In the second half, we study the limits of characters of certain induced representations of $G_{n}$ which are usually reducible. The limits turn out to be characters of $G$, and we analyse which of irreducible components are responsible to these limits.

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Takeshi Hirai. Etsuko Hirai. Akihito Hora. "Limits of characters of wreath products ${\mathfrak S}_{n}(T)$ of a compact group $T$ with the symmetric groups and characters of ${\mathfrak S}_{\infty}(T)$, I." Nagoya Math. J. 193 1 - 93, 2009.

Information

Published: 2009
First available in Project Euclid: 3 March 2009

zbMATH: 1182.22004
MathSciNet: MR2502908

Subjects:
Primary: 20C32
Secondary: 20C15 , 20E22 , 22A25 , 22C05 , 43A35

Rights: Copyright © 2009 Editorial Board, Nagoya Mathematical Journal

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