Méthode des Orbites et Représentations Quantiques

Details Méthode des Orbites et Représentations Quantiques Méthode des Orbites et Représentations Quantiques

2010-11-23

arxiv.org/abs/1011.5056v1

Mathematics

Symplectic Geometry

Th\`ese de Doctorat, Universit\'e de Provence, December 1996. viii+116 pages, 2 figures

Scientific paper

The first part of this thesis studies the notion of a "quantum representation", introduced by J.-M. Souriau in order to provide a polarization-free characterization of the Lie group representations attached to coadjoint orbits. When the group is compact, we show that Souriau's condition does indeed select the Borel-Weil representation within sections of the line bundle over an orbit. At the other extreme, for exponential solvable groups, we give counterexamples to an analogous assertion, but show that a refined condition does select the Kirillov-Bernat representation attached to an orbit. The second part develops the symplectic analogue of Mackey's normal subgroup analysis, using the notion of an induced hamiltonian G-space introduced by Kazhdan, Kostant and Sternberg.

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