Probability measures on families of partitions related to harmonic analysis on big wreath products

2025/05/13 by Strahov, Eugene
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.08394

Abstract

We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called the z-measures for the wreath product of a compact group with the symmetric group in the present paper. Our main result is an explicit formula for these z-measures which holds true for an arbitrary compact group. The result enables us to describe the spectral measures of the generalized regular representations of big wreath products.

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