Geodesic
Symplectic decomposition of the massive coadjoint orbits of a semidirect product
Serdica Mathematical Journal, Tome 43 (2017) no. 1, pp. 021-034.

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Let G be the semidirect product V ⋊ K where K is a connected semisimple non-compact Lie group acting linearily on a finite-dimensional real vector space V . Let O be a coadjoint orbit of G whose little group K0 is a maximal compact subgroup of K. We construct an explicit symplectomorphism between O and the symplectic product R^2n × O′ where O′ is a little group coadjoint orbit. We treat in details the case of the Poincaré group.
Keywords: Semidirect product, coadjoint orbit, unitary representation, symplectomorphism, Weyl quantization, Berezin quantization, Poincaré group, 81S10, 22E46, 22E45, 81R05 
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     author = {Cahen, Benjamin},
     title = {Symplectic decomposition of the massive coadjoint orbits of a semidirect product},
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     url = {http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a1/}
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Cahen, Benjamin. Symplectic decomposition of the massive coadjoint orbits of a semidirect product. Serdica Mathematical Journal, Tome 43 (2017) no. 1, pp. 021-034. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a1/