2016/12/12 by Friedrich Knop, Knop, Friedrich
Mathematics · #14M27 #53D20 #57S25 #Covariant Hamiltonian field theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Hamiltonian (control theory) #Hamiltonian system #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematical physics #Mathematics #Multiplicity (mathematics) #Physics #Pure mathematics #Representation Theory (math.RT) #Superintegrable Hamiltonian system #Symplectic Geometry (math.SG) #Symplectic geometry #Symplectic manifold #math.DG #math.RT #math.SG #msc:14M27 #msc:53D20 #msc:57S25
paper · pdf · doi:10.48550/arxiv.1612.03843
v1: 42 pages; v2: 42 pages, minor corrections, reference to a paper of Meinrenken added
openalex publication_date 2016/12/12 · arxiv created 2016/12/30 · arxiv updated 2017/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.