### Speaker

Hiroaki Kanno

### 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.