UNIVERSAL METAPLECTIC STRUCTURES AND GEOMETRIC QUANTIZATION

The recently developed concepts of generalized and universal spin structures are carried over from the orthogonal to the symplectic and unitary cases. It turns out that the analogues of Spinc-structures, namely the Mpc-structures and MUc-structures, are sufficient to avoid topological obstructions to their existence. It is indicated how this fact can be used in the geometric quantization of certain suitably polarized symplectic manifolds with arbitrary second Stiefel-Whitney class, where the usual Kostant-Souriau quantization scheme breaks down. © 1979 Springer-Verlag.