# The Dynamical equations for $\mathfrak{gl}(n\vert m)$

## TL;DR

This paper introduces a new set of compatible dynamical equations related to the $rak{gl}(n|m)$ algebra, linking them with the Knizhnik-Zamolodchikov equations and establishing a correspondence in this framework.

## Contribution

It proposes a compatible set of dynamical equations for $rak{gl}(n|m)$ and establishes the Matsuo-Cherednik correspondence in this context.

## Key findings

- Compatible dynamical equations commuting with KZ equations
- Extension of Matsuo-Cherednik correspondence to $rak{gl}(n|m)$
- Framework for future algebraic and integrable systems research

## Abstract

In this note we propose a compatible set of equations which commutes with the Knizhnik-Zamolodchikov equations based on the $\mathfrak{{gl}}(n\vert m)$ symmetry algebra and establish the Matsuo-Cherednik correspondence in this context.