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

Abstract

We obtain bilinear relations on Nekrasov partition functions, arising from study of tau functions of quantum $q$-Painlevé 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.

arXiv comment16 pages, 1 figure

References in corpus (7)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Cluster integrable systems, q-Painleve equations and their quantization
• Analyticity of Nekrasov Partition Functions
• Cluster Toda chains and Nekrasov functions
• CFT approach to the $q$-Painlevé VI equation
• Lectures on Instanton Counting
• Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations