Geometric Quantization and the Orbit Method


The orbit method is an object of pure mathematics, but it got a lot of impetus from physics under the heading of geometric quantization. Historically it was proposed by Kirillov in [Ki2] for the description of the unitary dual of nilpotent Lie groups. By fur- ther work of Kirillov and many others, in particular B. Kostant, M. Duflo, M. Vergne and D. Vogan, it grew into an important tool for explicit constructions of representations of various types of groups. The construction mechanism uses elements that also appear in theoretical physics when describing the transition from classical mechanics to quantum mechanics. We therefore start by recalling some of this background, even though we cannot give all the necessary definitions.


Line Bundle Heisenberg Group Symplectic Form Symplectic Manifold Elliptic Orbit 
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© Friedr. Vieweg & Sohn Verlag | GWV Fachverlage GmbH, Wiesbaden 2007

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