# Simply-laced quantum connections generalising KZ

## TL;DR

This paper introduces a new family of flat connections associated with simply-laced graphs, extending existing connections like KZ, Casimir, and dynamical connections through quantisation of isomonodromic deformation systems.

## Contribution

It constructs novel flat connections linked to simply-laced graphs by quantising Hamiltonian systems related to isomonodromic deformations.

## Key findings

- New flat connections generalising KZ, Casimir, and dynamical connections
- Connections derived via quantisation of isomonodromic deformation systems
- Applicable to simply-laced graphs

## Abstract

We construct a new family of flat connections generalising the KZ connection, the Casimir connection and the dynamical connection. These new connections are attached to simply-laced graphs, and are obtained via quantisation of time-dependent Hamiltonian systems controlling the isomonodromic deformations of meromorphic connections on the sphere.