Integrable Systems for Coadjoint Orbits of Classical Lie Algebras
Time: 2021-04-05
Published By: He Liu
Speaker(s): Yanpeng Li (University of Toronto)
Time: 16:00-17:00 April 6, 2021
Venue: Room 29, Quan Zhai, BICMR
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).
In this talk, I will present a new approach of constructing global action-angle coordinates for coadjoint orbits of classical Lie algebras. 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.
