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Twisted factorizations and multiple cluster structures in simple Lie groups

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CARW03 - Interdisciplinary applications of cluster algebras

We present a construction for cluster charts in simple Lie groups compatible with Poisson structures in the Belavin-Drinfeld classification. The key ingredient is a birational Poisson map from the group to itself that transform a Poisson  bracket associated with a nontrivial Belavin-Drinfeld data into the standard one.  It allows us to obtain a cluster chart as a pull-back of the Berenstein-Fomin-Zelevinsky cluster coordinates on the open double Bruhat cell. This is a joint work with M. Shapiro and A. Vainshtein.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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