Presentation
Primary Spaces
Gone Fishing Conference on Poisson Geometry
(2012)
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.
Keywords
- Primary spaces
Disciplines
Publication Date
September 30, 2012
Location
Los Angeles, CA
Citation Information
François Ziegler. "Primary Spaces" Gone Fishing Conference on Poisson Geometry (2012) Available at: http://works.bepress.com/francois_ziegler/6/