Unfolding of equivariant F-bundles and application to the mirror symmetry of flag varieties

TL;DR

This paper proves an unfolding theorem for equivariant F-bundles, extending Frobenius manifold theory, and applies it to establish mirror symmetry for the big quantum cohomology of flag varieties, linking recent small quantum cohomology results.

Contribution

It introduces a generalized unfolding theorem for equivariant F-bundles and applies it to prove mirror symmetry for flag varieties' big quantum cohomology.

Findings

Established an unfolding theorem for equivariant F-bundles.

Derived mirror symmetry for big quantum cohomology of flag varieties.

Connected small and big quantum cohomology mirror symmetry results.

Abstract

We establish an unfolding theorem for equivariant F-bundles (a variant of Frobenius manifolds), generalizing Hertling-Manin's universal unfolding of meromorphic connections. As an application, we obtain the mirror symmetry theorem for the big quantum cohomology of flag varieties, from the recent works on the small quantum cohomology mirror symmetry, via the equivariant unfolding theorem.