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14/11/2002, 13:30 — 14:30 — Room P3.10, Mathematics Building

Marco Mackaay, *Universidade do Algarve*

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

In my talks (17/10 and 14/11) I will sketch the construction of the
principal series of unitary representations of
$\mathrm{SL}(2,C)$ 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
$\mathrm{SL}(2,C)$.
### References

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