Milen Yakimov
UC Santa Barbara
Poisson Lie groups and Poisson homogeneous spaces

February 15, 4-5, MH 234

Abstract. The theory of Poisson Lie groups and their homogeneous spaces was developed extensively in the last 20 years. After Drinfeld's 1986 ICM talk it played crucial role in the representation theory of Hopf algebras by a generalization of the Kirillov-Kostant orbit method. It was further discovered that it explains in a uniform way the complete integrability of numerous dynamical systems. In this talk we will make an overview of these developments and will discuss the geometry of Poisson structures on simple algebraic groups and flag varieties. Both classes are (unexpectedly) related to classical and modern combinatorial structures as Schubert cells and cluster algebras. This talk is based on joint works with K. Brown and K. Goodearl.
Slobodan N. Simić
Last modified: Fri Feb 10 10:32:34 PST 2006