Séminaire Lotharingien de Combinatoire, 86B.71 (2022), 12 pp.
Charles Wang
Cluster Duality for Lagrangian and Orthgonal Grassmannians
Abstract.
In [Duke Math. J. 168 (2019), 3437-3527] Rietsch and Williams relate cluster structures and mirror symmetry for Grassmannians Gr(k,n), and use this 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 [arχiv:1304.4958].
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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