# Representation theory, gauge theory, and integrable systems

3-8 February 2019
Lecture Hall(1F), Kavli IPMU
Asia/Tokyo timezone

## Session

### Masahito Yamazaki: Discrete Painlevé Equation and Four-dimensional Gauge Theories

4 Feb 2019, 14:00
Lecture Hall(1F), Kavli IPMU

### Description

We discuss special solutions for the Hirota-type bilinear identity for the E8 discrete Painlevé equation and its "lens-generalization". The key identity is provided by transformation formulas for the lens-elliptic gamma function, which were first found via the Seiberg dualities in $4d$ $\mathcal{N}=1$ theories, and studied in connection with the super-master solution of the star-triangle relation.

### Presentation Materials

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