Vertex electrical model: lagrangian and non-negative properties

Abstract

This note is a modest addition to the work arXiv:2109.13952. Here we construct an embedding of the space of electrical networks to the totally non-negative Lagrangian Grassmannian in a generic situation with the help of the technique of vertex integrable models of statistical mechanics.

arXiv comment8 pages, 1 figure

References in corpus (6)

• Total positivity, Grassmannians, and networks
• Ising model and the positive orthogonal Grassmannian
• Electrical networks and Lie theory
• Electrical varieties as vertex integrable statistical models
• Electrical Networks, Lagrangian Grassmannians and Symplectic Groups
• Electrical networks and Lagrangian Grassmannians