# 1998 seminars

## 21/05/2004, Friday, 10:00–11:00

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