Quantization in Complex Symmetric Spaces

By means of the method described in the author's paper "Quantization" (Math. USSR Izv. 8 (1974), 1109-1165), we construct the quantization of a classical mechanics whose phase space is a classical complex symmetric space. We establish the important qualitative differences between the quantization of such mechanics and the quantization of ordinary mechanics with plane phase spaces: for all the spaces considered, except for the sphere, Planck's constant is bounded above. Moreover, in the compact case Planck's constant takes on only discrete values. Bibliography: 17 items.