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arXiv · 0901.0020

Poisson Geometry of Directed Networks in an Annulus

Michael Gekhtman·Michael Shapiro·Alek Vainshtein
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Abstract

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 in the Grassmannian. We then show that universal Poisson brackets introduced for the space of edge weights in arXiv: 0805.3541 induce a family of Poisson structures on rational-valued matrix functions and on the space of loops in the Grassmannian. In the former case, this family includes, for a particular kind of networks, the Poisson bracket associated with the trigonometric R-matrix.

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BibTeXRIS

Michael Gekhtman, Michael Shapiro, Alek Vainshtein. 2008-12-31. Poisson Geometry of Directed Networks in an Annulus. https://arxiv.org/abs/0901.0020

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