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Grassmannians and Cluster Algebras

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arxiv math/0311148 v1 pith:7XZQMOI7 submitted 2003-11-10 math.CO

Joshua S. Scott This is my paper · ORCID
classification math.CO
keywords clustergrassmannianstypealgebraalgebrasassociatedclassifiedconfigurations
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abstract

This paper demonstrates that the homogeneous coordinate ring of the Grassmannian $\Bbb{G}(k,n)$ 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 $\Bbb{R}\Bbb{P}^2$.

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  1. Singularities of massless scattering and cluster algebras

    hep-th 2025-07 conditional novelty 5.0 of 10

    Partial flag cluster algebras reproduce a large part of the two-loop five- and six-point massless scattering symbol alphabets, with the momentum twistor embedding stronger at six points after permutation completion.

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