Semidirect products and the Pukanszky condition

Details Semidirect products and the Pukanszky condition Semidirect products and the Pukanszky condition

1997-05-05

arxiv.org/abs/dg-ga/9705005v1

Mathematics

Differential Geometry

33 pages, including special macros and fonts (JGPpaper.tex is the source TeX file), to appear in J. Geom. Phys., also availabl

Scientific paper

10.1016/S0393-0440(97)00028-4

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.

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