|XXXII Workshop on Geometric Methods in Physics||30.06-6.07.2013|
Participants of Workshop
Participants of School
The Deformation Quantizations of the Hermitian Symmetric Space SU(1,n)/U(n)
In "The Deformation Quantizations of the Hyperbolic Plane" (Bieliavsky, Detournay, Spindel, Commun. Math. Phys. 2008), the authors show that a curvature contraction on the hyperbolic plane produces a symplectic symmetric surface whose transvection group is isomorphic to the Poincaré group in dimension 2. They also prove that from this contraction process emerges a differential operator of order two whose certain solutions of its evolution equation define convolution operators that intertwine the deformation theory (star-products) at the contracted level with that of the hyperbolic plane. This talk will be devoted to the study of a generalization of this construction in the case of the Hermitian symmetric space SU(1,n)/U(n).
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