Geometry Working Seminar

Aidan Patterson, Department of Pure Mathematics, University of Waterloo

"Thimm’s Trick and the Gelfand-Zeitlin System"

Thimm’s trick provides a method by which integrable systems constructed on the dual of a Lie algebra $\mathfrak{g}^{*}$ may be pulled back to integrable systems on a Hamiltonian G-space $(M,\omega, G, \Phi)$ using the moment map $\Phi$. The Gelfand-Zeitlin system represents “the best we can hope for” in terms of the integrable system that we may construct on $\mathfrak{g}^{*}$, and is itself a completely integrable system constructed on $\mathfrak{u}(n)^{*}$. In this talk we will prove Thimm’s trick, and construct the Gelfand-Zeitlin system. Time permitting, we will talk about some generalizations of Thimm’s trick to Hamiltonian G-spaces with Lu-moment maps.

MC 5413