Towards cluster duality for Lagrangian and orthogonal Grassmannians. (January 2023) - Wang, Charles
Abstract: In (2019 ), 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 Pech and Rietsch (2013) .