Quantum Hooks And Mirror Symmetry For Flag Varieties

Authors

Linda Chen, Swarthmore CollegeFollow
E. Kalashnikov

Document Type

Article

Publication Date

2023

Published In

Mathematische Zeitschrift

Abstract

Given a flag variety F1 (n; r₁,...,r_p), there is natural ring morphism from the symmetric polynomial ring in r₁ variables to the quantum cohomology of the flag variety. In this paper, we show that for a large class of partitions λ, the image of s_λ under the ring homomorphism is a Schubert class which is described by partitioning λ into a quantum hook (or q-hook) and a tuple of smaller partitions. We use this result to show that the Plücker coordinate mirror of the flag variety describes quantum cohomology relations. This gives new insight into the structure of this superpotential, and the relation between superpotentials of flag varieties and those of Grassmannians (where the superpotential was introduced by Marsh–Rietsch).

Comments

This work is a preprint that is freely available courtesy of Springer. The version of record can be freely accessed via SpringerNature's SharedIt service.

Recommended Citation

Linda Chen and E. Kalashnikov. (2023). "Quantum Hooks And Mirror Symmetry For Flag Varieties". Mathematische Zeitschrift. Volume 305, DOI: 10.1007/s00209-023-03359-7
https://works.swarthmore.edu/fac-math-stat/268