Duality for Knizhnik-Zamolodchikov and dynamical equations (Q1862247)

The authors show that under the \((\mathfrak{gl}_k,\mathfrak{gl}_n)\) duality the Knizhnik-Zamolodchikov and the quantized Knizhnik-Zamolodchikov equations for the Lie algebra \(\mathfrak{gl}_k\) exchange with the rational dynamical differential and the rational difference dynamical equations for the Lie algebra \(\mathfrak{gl}_n\) respectively and vice versa.