Blowup relations on $\mathbb{C}^2/\mathbb{Z}_2$ from Nakajima-Yoshioka blowup relations

TL;DR

This paper derives bilinear relations for Nekrasov partition functions related to quantum q-Painlevé tau functions, using Nakajima-Yoshioka blowup relations and algebraic methods, including modifications with Chern-Simons terms.

Contribution

It introduces an elementary algebraic approach to derive and prove new relations on Nekrasov partition functions from blowup relations.

Findings

Derived bilinear relations for Nekrasov partition functions.

Proved relations modified by Chern-Simons terms.

Connected blowup relations to quantum q-Painlevé tau functions.

Abstract

We obtain bilinear relations on Nekrasov partition functions, arising from study of tau functions of quantum $q$-Painlev\'e equations, from Nakajima-Yoshioka blowup relations by an elementary algebraic approach. Additionaly, using this approach, we prove certain relations on Nekrasov partition functions, modified by Chern-Simons term.