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Pedro Vaz, Universidade do Algarve

Induced representations and geometric quantization of coadjoint
orbits

There is a well known correspondence between the orbit method in
geometric quantization and the theory of unitary irreducible
representations of a Lie group. We show that the pre-quantization
of a coadjoint orbit of a connected Lie group G arises as the
infinitesimal version of an induced representation of G. With the
aid of a polarization, this procedure allow us to construct unitary
irreducible representations that are also the infinitesimal version
of an induced representation. As an example, we construct the
corresponding (infinite dimensional) unitary representations of the
Lie group SL(2,C), the universal cover of the Lorentz group.

References:

- I. M. Gelfand, M. I. Graev, and N. Ya. Vilenkin. Generalized Functions volume 5, "Integral Geometry and Representation Theory". Academic Press,New York, 1966.
- A.A. Kirillov. Elements of the Theory of Representations Springer-Verlag, 1976.
- N. Woodhouse. Geometric Quantization. Oxford, 1991.