Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 54, Number 4 (2014), 775-817.
Harmonic functions on the branching graph associated with the infinite wreath product of a compact group
A detailed study of the characters of , the wreath product of compact group with the infinite symmetric group , is indispensable for harmonic analysis on this big group. In preceding works, we investigated limiting behavior of characters of the finite wreath product as and its connection with characters of . This paper takes a dual approach to these problems. We study harmonic functions on , the branching graph of the inductive system of ’s, and give a classification of the minimal nonnegative harmonic functions on it. This immediately implies a classification of the characters of , which is a logically independent proof of the one obtained in earlier works. We obtain explicit formulas for minimal nonnegative harmonic functions on and Martin integral expressions for harmonic functions.
Kyoto J. Math., Volume 54, Number 4 (2014), 775-817.
First available in Project Euclid: 5 November 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20C32: Representations of infinite symmetric groups
Secondary: 20P05: Probabilistic methods in group theory [See also 60Bxx] 20E22: Extensions, wreath products, and other compositions [See also 20J05]
Hora, Akihito; Hirai, Takeshi. Harmonic functions on the branching graph associated with the infinite wreath product of a compact group. Kyoto J. Math. 54 (2014), no. 4, 775--817. doi:10.1215/21562261-2801822. https://projecteuclid.org/euclid.kjm/1415196156