Multiplicity free quasi-Hamiltonian manifolds

Abstract

A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free (twisted) quasi-Hamiltonian manifolds for simply connected compact Lie groups. As a result we recover old and find new examples of these structures.

v1: 42 pages; v2: 42 pages, minor corrections, reference to a paper of Meinrenken added

References in corpus (4)

• Introduction to the language of stacks and gerbes
• Classification of smooth affine spherical varieties
• Twisted conjugacy classes, coadjoint orbits of loop groups and D-branes in the WZW-model
• A new class of examples of group-valued moment maps

Cited by in corpus (1)

• Spinor modules for Hamiltonian loop group spaces