# Seminário de Teoria Quântica do Campo Topológica

### The coadjoint orbits of $\mathrm{SL}\left(2,C\right)$ - II

In my talks (17/10 and 14/11) I will sketch the construction of the principal series of unitary representations of $\mathrm{SL}\left(2,C\right)$ and the coadjoint orbits they correspond to. I will also try to explain the geometric quantization of these orbits and show that the infinitesimal representations thus obtained are indeed the ones corresponding to the principal series. If there is any time left I might say something about the Kirillov character formula for $\mathrm{SL}\left(2,C\right)$.

### References

1. I.M. Gelfand, R.A. Minlos, Z.Ya. Shapiro, Representations of the rotation and Lorentz groups and their applications, Pergamon Press, 1963.
2. A. Kirillov, Elements of representation theory, Springer.
3. G.W. Mackey, Induced representations of locally compact groups I, Ann. Math. 55(1):101-139, 1952.

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Organizadores correntes: José MourãoRoger PickenMarko Stošić

Mathseminars

Projectos FCT PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.