Séminaire de Géométrie et Quantification
(University of Notre-Dame and IHÉS)
Lundi 2 octobre 15h30 salle 201, IHP
Titre: Cluster structures on Poisson-Lie groups
Résumé :The connection between cluster algebras and Poisson structures is by now well-documented. Among the most important examples in which this connection has been utilized are coordinate rings of double Bruhat cells in semisimple Lie groups equipped with (the restriction of) the standard Poisson–Lie structure. In this talk, based on the joint work with M. Shapiro and A. Vainshtein, I will describe a construction of (generalized) cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson–Lie group GL(n), a generalized cluster structure on GL(n) compatible with the push-forward of the dual Poisson–Lie bracket and, time permitting, exotic cluster structures on GL(n) compatible with Poisson–Lie brackets arising from the Belavin-Drinfeld classification.