Towards cluster duality for Lagrangian and orthogonal Grassmannians. (January 2023)

• Record Type: Journal Article
• Authors: Wang, Charles
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 102
• Page End: 121
• Publication Date: 2023-01
• Subjects: Cluster Algebra -- Newton-Okounkov Body -- Plabic Graph; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.018
• Languages: English
• ISSNs: 0747-7171

Abstract

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) .