À¶Ý®ÊÓƵ

Justin Fus, University of À¶Ý®ÊÓƵ

The Geometry of the Based Loop Group and Moment Maps

Given a compact Lie group, we will explore a symplectic structure on the infinite-dimensional based loop group consisting of smooth maps from the circle to the Lie group with the identity as a basepoint. The maximal torus of the Lie group and the circle group together generate a Hamiltonian torus action on the loop group. Results on connectedness of level sets and convexity of the moment map, which are attempts to generalize those for finite-dimensional compact symplectic manifolds, will be previewed.

MC 5403