Primary Spaces, Mackey’s Obstruction etc.
March 27, 2012, update March 27, 2012
 
Joint work with Francois Ziegler. We call a hamiltonian N-space primary if its moment map is onto a single coadjoint orbit. The question has long been open whether such spaces always split as (homogeneous) × (trivial), as an analogy with representation theory might suggest. For instance, Souriau’s barycentric decomposition theorem asserts just this when N is a Heisenberg group. For general N, we give explicit examples which do not split, and show in- stead
 http://arxiv.org/abs/1203.5723http://arxiv.org/abs/1203.5723shapeimage_3_link_0
that primary spaces are always flat bundles over the coadjoint orbit. This provides the missing piece for a full “Mackey theory” of hamiltonian G-spaces, where G is an overgroup in which N is normal.