The University of Michigan Combinatorics Seminar
Winter 2011
April 8, 4:10-5:00, 3866 East Hall

Belavin-Drinfeld classification and
cluster structures on simple Lie groups

Michael Gekhtman

University of Notre Dame


We study natural cluster structures in the rings of regular functions on simple complex Lie groups, and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on G corresponds to a cluster structure in O(G). I will explaining how different parts of the conjecture are related to each other and present a supporting evidence that includes SL(n), n<5, as well as the standard Poisson-Lie structure on any simple G.