# KZ-Calogero correspondence revisited

## TL;DR

This paper revisits the relationship between the Knizhnik-Zamolodchikov equations for GL(N) and the n-particle quantum Calogero model, framing it as a quantization of the classical quantum Gaudin-Calogero correspondence.

## Contribution

It extends the quantum-classical correspondence to cases where the number of particles differs from the dimension N, providing a new perspective on the integrable models.

## Key findings

- Established a generalized KZ-Calogero correspondence for n ≠ N
- Provided a quantization framework linking quantum and classical integrable systems
- Enhanced understanding of the relationship between Gaudin and Calogero models

## Abstract

We discuss the correspondence between the Knizhnik-Zamolodchikov equations associated with $GL(N)$ and the $n$-particle quantum Calogero model in the case when $n$ is not necessarily equal to $N$. This can be viewed as a natural "quantization" of the quantum-classical correspondence between quantum Gaudin and classical Calogero models.