Benjamin Hoffman, Cornell University
3:30 PM - 4:30 PM
The Gelfand-Zeitlin system is a completely integrable system on the Poisson manifold , which has an elegant and elementary description due to Guillemin and Sternberg. It is an open problem to construct analogous integrable systems on , for other compact Lie algebras . I will present progress towards such a construction.
The moment map image of the Gelfand-Zeitlin system is a polyhedral cone, and integral points of this cone parametrize canonical bases for irreducible representations of . Our approach is to consider analogous polyhedral cones, described by Berenstein, Kazhdan, and Zelevinsky, which parametrize canonical bases for irreducible representations of of other type.
This is based on joint works with Alekseev, Berenstein, Lane, and Li.
Event contact: sema dot salur at rochester dot edu