A Plücker coordinate mirror for type A flag varieties

We introduce a superpotential for partial flag varieties of type A $A$ . This is map W : Y ∘ → C $W: Y^\circ \rightarrow \mathbb {C}$ , where $Y^\circ$ the complement an anticanonical divisor on product Grassmannians. The $W$ expressed in terms Plücker coordinates Grassmannian factors. construction generalizes Marsh–Rietsch coordinate mirror show that distinguished cluster chart $Y$ our agrees with earlier mirrors constructed by Eguchi–Hori–Xiong and Batyrev–Ciocan-Fontanine–Kim–van Straten. Our main tool quantum Schubert calculus variety.