Geometry Seminar

Tropical Poisson-Lie Groups

Benjamin Hoffman, Cornell University

Monday, November 19th, 2018
3:30 PM - 4:30 PM
Hylan 1106A

The Gelfand-Zeitlin system is a completely integrable system on the Poisson manifold $\mathfrak{u}(n)^*$, which has an elegant and elementary description due to Guillemin and Sternberg. It is an open problem to construct analogous integrable systems on $\mathfrak{k}^*$, for other compact Lie algebras $\mathfrak{k}$. 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 $\mathfrak{u}(n)$. Our approach is to consider analogous polyhedral cones, described by Berenstein, Kazhdan, and Zelevinsky, which parametrize canonical bases for irreducible representations of $\mathfrak{k}$ of other type.

This is based on joint works with Alekseev, Berenstein, Lane, and Li.

Event contact: sema dot salur at rochester dot edu