Grassmannians and Cluster Algebras

2003/11/10 by Joshua S. Scott, Scott, Joshua S. · 15 citations
Chemistry · Mathematics · Physics and Astronomy · #14M99 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Chemistry #Cluster (spacecraft) #Cluster algebra #Combinatorics #Combinatorics (math.CO) #Computer science #Connection (principal bundle) #FOS: Mathematics #Geometry #Grassmannian #Homogeneous #Mathematics #Nonlinear Waves and Solitons #Physics #Point (geometry) #Pure mathematics #Quantum mechanics #Ring (chemistry) #Type (biology) #math.CO #msc:14M99

paper · pdf · doi:10.48550/arxiv.math/0311148

published in arXiv (Cornell University) (Cornell University) · 58 pages

arxiv created 2003/11/10 · openalex publication_date 2003/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper demonstrates that the homogeneous coordinate ring of the Grassmannian \BbbG(k,n) is a \it cluster algebra of geometric type - as defined by S. Fomin and A. Zelevinsky. Grassmannians having \it finite cluster type are classified and the associated cluster variables are studied in connection with the geometry of configurations of points in ℝℙ².

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• A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology
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• Web Diagrams of Cluster Variables for Grassmannian Gr(4,8)
• Spectral networks for polynomial cubic differentials
• Singularities of massless scattering and cluster algebras
• From dual canonical bases to positroidal subdivisions
• Symbol Alphabets in QCD and Flag Cluster Algebras
• Cluster automorphism group of braid varieties
• Ind-cluster algebras and infinite Grassmannians
• A note on a cluster structure of the coordinate ring of a simple algebraic group

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