# Duality for Knizhnik-Zamolodchikov and Dynamical Operators

## TL;DR

This paper explores the duality between Knizhnik-Zamolodchikov and dynamical operators, demonstrating their natural exchange in the context of _{k}, _{n}-duality on polynomial spaces with anticommuting variables.

## Contribution

It establishes a new duality relation showing how these operators interchange under _{k}, _{n}-duality in a polynomial setting with anticommuting variables.

## Key findings

- Operators exchange under duality.
- Duality relates differential and difference operators.
- Results deepen understanding of algebraic symmetries.

## Abstract

We consider the Knizhnik-Zamolodchikov and dynamical operators, both differential and difference, in the context of the $(\mathfrak{gl}_{k}, \mathfrak{gl}_{n})$-duality for the space of polynomials in $kn$ anticommuting variables. We show that the Knizhnik-Zamolodchikov and dynamical operators naturally exchange under the duality.