The Dynamical equations for $\mathfrak{g}\mathfrak{l}(n\mathrm{\mid }m)$

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