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
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.