# QKZ-Ruijsenaars correspondence revisited

## TL;DR

This paper revisits the correspondence between quantum Knizhnik-Zamolodchikov equations and Ruijsenaars models, exploring their quantum and classical relationships and extending the understanding of integrable systems.

## Contribution

It provides a detailed analysis of the Matsuo-Cherednik correspondence for $GL(N)$ and extends the quantum-classical correspondence to broader settings.

## Key findings

- Established a link between quantum KZ equations and Ruijsenaars models.
- Extended the quantum-classical correspondence to non-equal particle and spin chain sizes.
- Clarified the role of the quasiclassical limit in integrable systems.

## Abstract

We discuss the Matsuo-Cherednik type correspondence between the quantum Knizhnik-Zamolodchikov equations associated with $GL(N)$ and the $n$-particle quantum Ruijsenaars model, with $n$ being not necessarily equal to $N$. The quasiclassical limit of this construction yields the quantum-classical correspondence between the quantum spin chains and the classical Ruijsenaars models.