#### Title

Primary Spaces

#### Document Type

Presentation

#### Publication Date

9-30-2012

#### 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.

#### Sponsorship/Conference/Institution

Gone Fishing Conference on Poisson Geometry

#### Location

Los Angeles, CA

#### Recommended Citation

Ziegler, François.
2012.
"Primary Spaces."
*Mathematical Sciences Faculty Presentations*.
Presentation 583.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/583