Monadicity of localization for Lie super-algebras $\mathfrak{gl}(m, n)$

Abstract

We study the localization functor from the category of representation of Lie super-algebra $\mathfrak{g} = \mathfrak{gl}(m, n)$ into monodromic D-modules on the flag manifold $X = G/B$. We show that the right localization is monadic in a suitable sense, which identifies the coderived category of $\mathfrak{g}$-modules with the ind-completion of compactly generated $W$-modules for some algebra $W$ in monodromic $D_X$-bimodules.