# Representation theory, gauge theory, and integrable systems

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

## Session

### Hiroaki Kanno: 3d holomorphic blocks from the intertwiner of quantum toroidal algebra

5 Feb 2019, 11:00
Lecture Hall(1F), Kavli IPMU

### Description

The intertwiner of the Fock representation of the quantum toroidal algebra of $\mathfrak{gl}_1$ type can be identified with the refined topological vertex, which is a building block of 5d lift of the Nekrasov instanton partition function. In general the correlation function of the intertwiners satisfies a difference equation of KZ type, where the associated R-matrix is featured. In this talk I will explain how we can derive generalized KZ equation for quantum toroidal algebra in a simplified setting and show that 3d holomorphic blocks arise as solutions to the equation.

### Presentation Materials

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