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Limits of Characters of Wreath Products 𝔖n(T) of a Compact Group T With the Symmetric Groups and Characters of 𝔖∞(T), I

Published online by Cambridge University Press:  11 January 2016

Takeshi Hirai ,
Etsuko Hirai  and
Akihito Hora
Takeshi Hirai
Affiliation:
22-8 Nakazaichi-Cho, Iwakura, Sakyo-Ku, Kyoto 606-0027, Japan, hirai.takeshi@math.mbox.media.kyoto-u.ac.jp
Etsuko Hirai
Affiliation:
Department of Mathematics, Faculty of Sciences, Kyoto Sangyo University, Kita-Ku, Kyoto 603-8555, Japan, hiraietu@cc.kyoto-su.ac.jp
Akihito Hora
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-Ku, Nagoya 464-8602, Japan, hora@math.nagoya-u.ac.jp
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Abstract

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In the first half of this paper, all the limits of irreducible characters of Gn = 𝔖n(T) as n → ∞ are calculated. The set of all continuous limit functions on G = 𝔖 ∞(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 Gn 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 Gn 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.

Keywords

20C3220C1520E2222A2522C0543A35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 193 , 2009 , pp. 1 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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