349 citations · 768 across the 43 of their papers we have counts for
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Poisson structures compatible with the cluster algebra structure in Grassmannians
Michael Gekhtman, Michael Shapiro, Alexander Stolin +1
We describe all Poisson brackets compatible with the natural cluster algebra structure in the open Schubert cell of the Grassmannian and show that any such bracket endows…
Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
We present the third in the series of papers describing Poisson properties of planar directed networks in the disk or in the annulus. In this paper we concentrate on special networ…
Poisson Geometry of Directed Networks in an Annulus
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
As a generalization of Postnikov's construction (see arXiv: math/0609764), we define a map from the space of edge weights of a directed network in an annulus into a space of loops…