Towards cluster duality for Lagrangian and orthogonal Grassmannians

被引：1

作者：

Wang, Charles ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2023年 / 114卷

关键词：

Cluster Algebra; Newton-Okounkov Body; Plabic Graph; NEWTON-OKOUNKOV BODIES;

D O I：

10.1016/j.jsc.2022.04.018

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 poly-tope obtained from the superpotential defined by Pech and Rietsch on the mirror Orthogonal Grassmannian in Pech and Rietsch (2013). (C)& nbsp;2022 Elsevier Ltd. All rights reserved.

引用

页码：102 / 121

页数：20

共 16 条

[11] Matching polytopes, toric geometry, and the totally non-negative Grassmannian [J].