Functional equations of Nekrasov functions proposed by Ito-Maruyoshi-Okuda

TL;DR

This paper proves functional equations for Nekrasov partition functions associated with A1-singularity, using wall-crossing formulas and methods developed by Nakajima-Yoshioka and Mochizuki.

Contribution

It provides a rigorous proof of the functional equations of Nekrasov functions for A1-singularity, confirming conjectures by Ito-Maruyoshi-Okuda.

Findings

Established functional equations for Nekrasov partition functions

Applied wall-crossing formulas in the proof

Extended the mathematical understanding of Nekrasov functions

Abstract

We prove functional equations of Nekrasov partition functions for $A_{1}$-singularity, suggested by Ito-Maruyoshi-Okuda. Our proof uses the method by Nakajima-Yoshioka based on the theory of wall-crossing formula developed by Mochizuki.