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arXiv · 2011.08093

A Pl\"ucker coordinate mirror for type A flag varieties

Elana Kalashnikov
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Abstract

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

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Elana Kalashnikov. 2020-11-16. A Pl\"ucker coordinate mirror for type A flag varieties. https://arxiv.org/abs/2011.08093

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