(Quasi-)Hamiltonian manifolds of cohomogeneity one
arXiv:1910.01947 · doi:10.1007/s00209-023-03325-3
Abstract
We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). Here the group acting is a compact connected Lie group (simply connected in the quasi-Hamiltonian case). This work is a concretization of the more general classification (arXiv:1612.03843) of multiplicity free manifolds in the special case of rank one. As a result we obtain numerous new concrete examples of multiplicity free quasi-Hamiltonian manifolds or, equivalently, Hamiltonian loop group actions.
v1: 24 pages, this paper replaces arXiv:1712.09036; v2: 26 pages, minor changes; v3: 25 pages, final version
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