Room P4.35, Mathematics Building

Róbert Szőke, Eötvös Loránd University (ELTE)
Adapted polarizations

Polarizations (real or complex) play an important role in geometric quantization. The adapted Kähler structure is a natural complex polarization on  the phase space $N$ of a Riemannian manifold. It turns out, that this Kähler structure is just one member of a family of (real or complex) polarizations parameterized by the complex plane, due to the symmetries of $N$. In fact to talk about these polarizations one doesn't need a Riemannian metric, a connection suffices. In the talk I shall discuss joint results with Lempert concerning these polarizations.