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HARMONIC FUNCTIONS ON THE BRANCHING GRAPH ASSOCIATED WITH THE INFINITE WREATH PRODUCT OF A COMPACT GROUP

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84170

Title: HARMONIC FUNCTIONS ON THE BRANCHING GRAPH ASSOCIATED WITH THE INFINITE WREATH PRODUCT OF A COMPACT GROUP
Authors: HORA, Akihito Browse this author
HIRAI, Takeshi Browse this author
Keywords: the infinite symmetric group
wreath product
branchinh hraph
harmonic function
Martin boundary
character
factor representation
Issue Date: 12-Dec-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1024
Start Page: 1
End Page: 36
Abstract: Detailed study of the characters of S∞(T)S∞(T), the wreath product of compact group T with the infinite symmetric group S∞, is indispensable for harmonic analysis on this big group. In preceding works, we investigated limiting behavior of characters of the finite wreath product Sn(T) as n→∞ and its connection with characters of S∞(T). This paper takes a dual approach to these problems. We study harmonic functions on Y(Tˆ), the branching graph of the inductive system of Sn(T)'s, and give a classification of the minimal nonnegative harmonic functions on it. This immediately implies a classification of the characters of S∞(T), which is a logically independent proof of the one obtained in earlier works. We obtain explicit formulas for minimal nonnegative harmonic functions on Y(Tˆ) and Martin integral expressions for harmonic functions.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69829
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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