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Hokkaido University Preprint Series in Mathematics >
HARMONIC FUNCTIONS ON THE BRANCHING GRAPH ASSOCIATED WITH THE INFINITE WREATH PRODUCT OF A COMPACT GROUP
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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