Grassmannians and Cluster Algebras

2003/11/10 by Joshua S. Scott, Scott, Joshua S. · 12 citations
Mathematics · #14M99 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:14M99

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

58 pages

arxiv created 2003/11/10 · arxiv updated 2009/12/01

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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• Super Higher-Teichmüller Geometry and Loop Amplitudes
• Frieze patterns in representation theory
• A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology
• Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras
• 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

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