Abstract
We call a Hamiltonian N-space primary if its equivariant momentum map is onto a single coadjoint orbit, U. In other words, such a space is as far as can be from multiplicity-free. When N is a Heisenberg group, Souriau’s ‘barycentric decomposition theorem’ shows that all primary spaces are products of (coverings of) U with trivial N-spaces. For general N, the question whether such a factorization survives has long been open. In the present work we give 1) examples where factorization fails, and 2) a structure theorem extending Souriau’s to general N. This provides the missing piece for a full ‘Mackey theory’ of Hamiltonian G-spaces, where G is an overgroup in which N is normal.
Original language | American English |
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State | Published - Jun 2012 |
Event | Souriau’s 90 Conference - Aix-en-Provence, France Duration: Jun 1 2012 → … |
Conference
Conference | Souriau’s 90 Conference |
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Period | 06/1/12 → … |
Disciplines
- Mathematics
Keywords
- Hamiltonian N-space
- Mackey theory
- Primary spaces
- Souriau