Semidirect products and the Pukanszky condition
Abstract
We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained by symplectic induction on some coadjoint orbit of a "smaller" Lie group. We study also a special class of polarizations related to a semidirect product and the validity of Pukanszky's condition for these polarizations. Some examples of physical interest are discussed using the previous methods.
Keywords
Cite
@article{arxiv.dg-ga/9705005,
title = {Semidirect products and the Pukanszky condition},
author = {P. Baguis},
journal= {arXiv preprint arXiv:dg-ga/9705005},
year = {2009}
}
Comments
33 pages, including special macros and fonts (JGPpaper.tex is the source TeX file), to appear in J. Geom. Phys., also available via anonymous ftp or via gopher gopher://cpt.univ-mrs.fr/