Cluster Duality for Lagrangian and Orthogonal Grassmannians
Combinatorics
2021-02-02 v1
Abstract
In [RW19] Rietsch and Williams relate cluster structures and mirror symmetry for type A Grassmannians Gr(k, n), and use this interaction to construct Newton-Okounkov bodies and associated toric degenerations. In this article we define a cluster seed for the Lagrangian Grassmannian, and prove that the associated Newton-Okounkov body agrees up to unimodular equivalence with a polytope obtained from the superpotential defined by Pech and Rietsch on the mirror Orthogonal Grassmannian in [PR13].
Keywords
Cite
@article{arxiv.2102.01054,
title = {Cluster Duality for Lagrangian and Orthogonal Grassmannians},
author = {Charles Wang},
journal= {arXiv preprint arXiv:2102.01054},
year = {2021}
}
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19 pages