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The $D_{\hslash}$-module mirror conjecture for flag varieties
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abstract
Rietsch constructed a candidate $T$-equivariant mirror LG model for any flag variety $G/P$. In this paper, we prove the following mirror symmetry prediction: the small $T\times\mathbb{G}_m$-equivariant quantum cohomology of $G/P$ equipped with quantum $\hslash$-connection is isomorphic as $D_{\hslash}$-modules to the Brieskorn lattice associated to the LG model equipped with Gauss-Manin $\hslash$-connection.
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Unfolding of equivariant F-bundles and application to the mirror symmetry of flag varieties
Big quantum D-module mirror symmetry for flag varieties G/P follows from small mirror symmetry via a new unfolding theorem for equivariant F-bundles.
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