The $D_{\mathrm{\hslash }}$-module mirror conjecture for flag varieties

Rietsch constructed a candidate $T$-equivariant mirror LG model for any flag variety $G\mathrm{/}P$. In this paper, we prove the following mirror symmetry prediction: the small $T\times {\mathbb{G}}_m$-equivariant quantum cohomology of $G\mathrm{/}P$ equipped with quantum $\mathrm{\hslash }$-connection is isomorphic as $D_{\mathrm{\hslash }}$-modules to the Brieskorn lattice associated to the LG model equipped with Gauss-Manin $\mathrm{\hslash }$-connection.