  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.
