Duality for Knizhnik-Zamolodchikov and Dynamical Operators

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.