Knizhnik-Zamolodchikov equations in Deligne categories

Abstract

We consider the Knizhnik-Zamolodchikov equations in Deligne Categories in the context of $({\mathfrak{gl}}_m,{\mathfrak{gl}}_n)$ and $({\mathfrak{so}}_m,{\mathfrak{so}}_{2n})$ dualities. We derive integral formulas for the solutions in the first case and compute monodromy in both cases.