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Grassmannian cluster algebras

WebJul 1, 2024 · A finite cluster algebra provides a natural triangulation for the tropical … WebDec 19, 2024 · Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scattering amplitudes in physics. In this paper, we apply the tableaux method to classify cluster variables in Grassmannian cluster algebras …

[math/0311148] Grassmannians and Cluster Algebras

WebDec 23, 2016 · This paper follows the program of study initiated by S. Fomin and A. Zelevinsky, and demonstrates that the homogeneous coordinate ring of the Grassmannian G(k, n) is a cluster algebra of geometric type.Those Grassmannians that are of finite cluster type are identified and their cluster variables are interpreted geometrically in … WebWeb bases in the sl2 and sl3 cases are important in cluster algebra structure of Grassmannian coordinate rings [FP16, Fra20]. While cluster algebras from coordinate rings of partial ag varieties (e.g., [GLS08]) have been comparatively less studied, we believe that the pieces of these coordinate cynthia kershner https://a-kpromo.com

Grassmannians and Cluster Structures SpringerLink

WebMay 23, 2014 · 1. Introduction. Since cluster algebras were introduced by Fomin and Zelevinsky [], it has been recognized that cluster algebra structures on homogeneous coordinate rings on Grassmannians are among the most important classes of examples.The demonstration of the existence of such a structure is due to Scott [] and one reason for … WebApr 16, 2024 · Categorification and the quantum Grassmannian. In \cite {JKS} we gave an (additive) categorification of Grassmannian cluster algebras, using the category $\CM (A)$ of Cohen-Macaulay modules for a certain Gorenstein order . In this paper, using a cluster tilting object in the same category $\CM (A)$, we construct a compatible pair , … WebNov 10, 2003 · Grassmannians and Cluster Algebras. This paper demonstrates that … cynthia keverian

[1907.13575] Quantum affine algebras and …

Category:[1907.01053] Tropical Grassmannians, cluster algebras and scattering ...

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Grassmannian cluster algebras

Quantum affine algebras and Grassmannians Request PDF

WebJun 21, 2024 · Quivers with potentials for Grassmannian cluster algebras Part of: … WebFeb 1, 2024 · The action is by quasi-automorphisms of the cluster structure on the …

Grassmannian cluster algebras

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WebWhat do cluster algebras tell us about Grassmannians? One of the first examples of a cluster algebra given in Fomin and Zelevinsky's original paper is the homogeneous coordinate ring C [ G 2, n] of the Grassmannian of planes in C n. It has also been shown by Scott that C [ G k, n] carries a cluster algebra structure for any k. WebDefinition, basic properties and examples of cluster algebras. Combinatorics of root …

WebIt is shown that many results on cluster algebras (the Laurent phenomenon, the classification of finite-type cluster algebras) extend to the quantum case. The important open problem is to show that quantum cluster monomials have non-negative coefficients. The paper under review deals with skew-symmetric acyclic quantum cluster algebras. The WebCluster algebras are an extremely new mathematical structure, discovered in 2002 by …

WebBULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY S 0273-0979(2013)01417-4 Article electronically published on June 10, 2013 CLUSTER ALGEBRAS: AN INTRODUCTION WebLet us first motivate the need for a notion of distance in a cluster algebra, concentrating on the example of the Grassmannian. A pair of Plücker coordinates can appear together in the same cluster if and only if they are labeled by weakly separated subsets of [n] delimited-[] 𝑛 [n] [ italic_n ].For Plücker coordinates that do not appear together in the same cluster, …

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WebFeb 27, 2024 · An action of the extended affine braid group on Grassmannian cluster … billy walters computer groupWebGRASSMANNIANS AND CLUSTER ALGEBRAS 1. Introduction This paper follows the … cynthia keveneyWebJul 13, 2016 · A categorification of Grassmannian cluster algebras - Jensen - 2016 - … billy walters book mickelsonWebJul 1, 2024 · We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians ${\\rm Gr}(k,n)$. A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose volume computes the scattering amplitudes. Using this method … billy walters betting systemWebFeb 20, 2006 · This paper follows the program of study initiated by S. Fomin and A. … billy walters daughterWebJul 29, 2024 · Download a PDF of the paper titled Families of Gr\"obner Degenerations, Grassmannians and Universal Cluster Algebras, by Lara Bossinger and 1 other authors. ... We apply this construction to the Grassmannians ${\rm Gr}(2,\mathbb C^n)$ with their Plücker embeddings and the Grassmannian ${\rm Gr}\big(3,\mathbb C^6\big)$ with its … cynthia keyesWebJul 28, 2024 · We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian category of infinite rank is given as the category of graded maximal Cohen-Macaulay modules over a certain hypersurface singularity. We show that … billy walters gambler new book