Symmetries on plabic graphs and associated polytopes
Xin Fang, Ghislain Fourier
TL;DR
This paper explores the relationship between symmetries in plabic graphs and the polytopes associated with Grassmann varieties, revealing how dualities between different polytopes originate from positive structures.
Contribution
It uncovers the connection between symmetries on plabic graphs and dualities of polytopes in Grassmann varieties through positive structures.
Findings
Duality between Gelfand-Tsetlin and Feigin-Fourier-Littelmann-Vinberg polytopes explained
Symmetries on plabic graphs linked to polytope dualities
Positive structures underpin the duality relationships
Abstract
For Grassmann varieties, we explain how the duality between the Gelfand-Tsetlin polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes arises from different positive structures.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory