Quantum Co-Adjoint Orbits of the Group of Affine Transformations of the Complex Straight Line

摘要

We construct start-products on the co-adjoint orbit of Lie group $\Aff({\bfC})$ of affine transformations of the complex straight line and apply them toobtain the irreducible unitary representations of this group. These resultsshow effectiveness of the Fedosov quantization even for groups which areneither nilpotent nor exponential. Together with the result for the group$\Aff({\bf R})$ in math.QA/9905002, we have thus a description of quantum$\bar{MD}$ co-adjoint orbits.