Semidirect Products and the Pukanszky Condition
نویسنده
چکیده
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.
منابع مشابه
Semidirect Products and the Pukanszky Condition
33 7] Kostant, B.: On certain unitary representations which arise from a quantization theory, in \Group representations in mathematics and physics", 32 p. baguis of k C p = so(3) C , where A 7 ! ^ A is the natural isomorphism so(3) C = (R 3) C. These subspaces have complex dimension one and are such that a + 0 a ? 0 (k p) C = k C p. Furthermore, it is elementary to verify that a + 0 ; a + 0 ] (...
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