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arXiv · 2505.08394

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

Eugene Strahov
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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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Eugene Strahov. 2025-05-13. Probability measures on families of partitions related to harmonic analysis on big wreath products. https://arxiv.org/abs/2505.08394

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