Jack combinatorics of the equivariant edge measure

TL;DR

This paper establishes a combinatorial equivalence between the equivariant edge measure, relevant in Donaldson-Thomas invariants of toric threefolds, and the Jack-Plancherel measure, revealing a deep connection in geometric representation theory.

Contribution

It demonstrates that the equivariant edge measure is, up to conventions, equivalent to the Jack-Plancherel measure, providing new insights into their relationship.

Findings

Equivariant edge measure equals Jack-Plancherel measure under certain conventions.

Provides a combinatorial proof of the measure equivalence.

Links geometric invariants to classical symmetric function measures.

Abstract

We study the equivariant edge measure: a measure on partitions which arises implicitly in the edge term in the localization computation of the Donaldson-Thomas invariants of a toric threefold. We combinatorially show that the equivariant edge measure is, up to choices of convention, equal to the Jack-Plancherel measure.