Towards cluster duality for Lagrangian and orthogonal Grassmannians

In (), 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...
Ausführliche Beschreibung

In (), 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 . Ausführliche Beschreibung