Representation Theory and Mathematical Physics Seminar: New action-angle variables on coadjoint orbits

Seminar | April 10 | 4-5 p.m. | 939 Evans Hall

 Yanpeng Lie, University of Geneva

 Department of Mathematics

The problem of constructing global action-angle variables on coadjoint orbits of compact Lie groups is one of the interesting questions in the theory of integrable systems. A fundamental contribution was made by Guillemin-Sternberg who constructed the Gelfand-Zeitlin integrable systems on coadjoint orbits of the groups \(SU(n)\) and \(SO(n)\). Recently, toric degeneration techniques allowed for the construction of global action-angle variables on rational coadjoint orbits of compact Lie groups of all types.

In this talk, I will present a new approach which aims at constructing global action-angle coordinates on all regular coadjoint orbits of compact Lie groups and on a large family of related Hamiltonian spaces. It combines the results of Ginzburg-Weinstein on the theory of Poisson-Lie groups and the theory of cluster algebras using the "partial tropicalization” procedure.

The talk is based on joint works with A. Alekseev, A. Berenstein, B. Hoffman, and J. Lane.

 artamonov@berkeley.edu