Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty),H(\infty))$

TL;DR

This paper explores z-measures on partitions with specific deformation parameters, explaining their representation-theoretic origins and significance in harmonic analysis on the infinite symmetric group.

Contribution

It provides a detailed explanation of the representation-theoretic origin of z-measures with deformation parameters 2 or 1/2 and their role in harmonic analysis.

Findings

Clarifies the connection between z-measures and infinite Gelfand pairs.

Elucidates the role of these measures in harmonic analysis on infinite symmetric groups.

Provides a detailed theoretical framework for understanding these measures.

Abstract

The paper deals with the z-measures on partitions with the deformation (Jack) parameters 2 or 1/2. We provide a detailed explanation of the representation-theoretic origin of these measures, and of their role in the harmonic analysis on the infinite symmetric group.