THE REPRESENTATIONS OF LIE-GROUPS AND GEOMETRIC QUANTIZATIONS

In this paper we discuss the relation between representations of Lie g roups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic d iscrete series of representations and spherical representations of red uctive Lie groups are constructed by geometric quantizations of ellipt ic and hyperbolic coadjoint orbits.