Year: 2009
Type: preprint
Abstract: We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical correspondence between the orbit spaces of the respective moment images. Furthermore, we show that reduced spaces with respect to the action of one group are symplectomorphic to coadjoint orbits of the other group. In the Kaehler case we show that the linear representation of a pair of compact Lie groups on the geometric quantization of the manifold is then equipped with a representation-theoretic Howe duality.
Source: arXiv (Cornell University)
Authors: Balleier, Carsten, Wurzbacher, Tilmann
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5738355574
OpenAlex ID: W2951137498