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Cluster algebras and Poisson geometry

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arxiv math/0208033 v2 pith:4J7QASOR submitted 2002-08-05 math.QA math.AGmath.COmath.SG

M. Gekhtman , M. Shapiro , A. Vainshtein This is my paper · ORCID
classification math.QAmath.AGmath.COmath.SG
keywords clusterpoissontoricactionalgebrascompatiblecomponentscompute
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We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of connected components of refined open Bruhat cells in Grassmanians G(k,n) over real numbers.

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  1. Cluster Adjacency for m=2 Yangian Invariants

    hep-th 2019-08 conditional novelty 6.0 of 10

    Every m=2 Yangian invariant is labelled by a collection of non-intersecting polygons in an n-gon, yielding an explicit formula whose denominator factors lie in a common Gr(2,n) cluster, thus manifestly satisfying clus...

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