Limits of characters of wreath products *_n(T) of a compact group T with the symmetric groups and characters of *_∞(T), II From a viewpoint of probability theory

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概要

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• This paper is the second part of our study on limiting behavior of characters of wreath products \mathfrak{S}n(T) of compact group T as n → ∞ and its connection with characters of \mathfrak{S}∞(T). Contrasted with the first part, which has a representation-theoretical flavor, the approach of this paper is based on probabilistic (or ergodic-theoretical) methods. We apply boundary theory for a fairly general branching graph of infinite valencies to wreath products of an arbitrary compact group T. We show that any character of \mathfrak{S}∞(T) is captured as a limit of normalized irreducible characters of \mathfrak{S}n(T) as n → ∞ along a path on the branching graph of \mathfrak{S}∞(T). This yields reconstruction of an explicit character formula for \mathfrak{S}∞(T).

• 社団法人 日本数学会の論文
• 2008-10-01

著者

• Hirai Etsuko

  Department Of Mathematics Faculty Of Science Kyoto Sangyo University

• Hora Akihito

  Graduate School Of Mathematics Nagoya University

• Hirai Takeshi

  unknown

関連論文

• A NOTE ON THE FIRST HOMOLOGY OF THE GROUP OF POLYNOMIAL AUTOMORPHISMS OF THE COORDINATE SPACE
• Limits of characters of wreath products *_n(T) of a compact group T with the symmetric groups and characters of *_∞(T), II From a viewpoint of probability theory

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