Primary Spaces, Mackey’s Obstruction, and the Generalized Barycentric Decomposition
Let a Lie group G act on a symplectic manifold X in Hamiltonian fashion, i.e., the action preserves the 2 form of X and we have an equivariant momentum map X > Lie(G)*. If N is a normal subgroup of G, "Symplectic Mackey Theory" reduces the study of such actions to that of i) coadjoint orbits of N and ii) symplectic actions of subgroups of G/N. Just as its cousin in representation theory, this analysis has 3 steps of which the last concerns the "primary" situation where X > Lie(G)* > Lie(N)* is onto a single coadjoint orbit U of N. So far this step had only been elucidated in the case where X splits as a product U x Z. In this talk I will describe joint work with P. Iglesias showing that (1) X does not always split in this way; (2) X is always a flat bundle over U. This enables us to complete the Mackey analysis in the general case.
Georgia Southern University Mathematical Sciences Colloquium
"Primary Spaces, Mackey’s Obstruction, and the Generalized Barycentric Decomposition."
Mathematical Sciences Faculty Presentations.