A Pl\"ucker coordinate mirror for partial flag varieties and quantum Schubert calculus
Abstract
We construct a Pl\"ucker coordinate superpotential F- that is mirror to a partial flag variety F(n). Its Jacobi ring recovers the small quantum cohomology of F(n) and we prove a folklore conjecture in mirror symmetry. Namely, we show that the eigenvalues for the action of the first Chern class c1( F(n)) on quantum cohomology are equal to the critical values of F-. We achieve this by proving new identities in quantum Schubert calculus that are inspired by our formula for F- and the mirror symmetry conjecture.
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