The representations of Lie groups and geometric quantizations (Q1270334)

The author constructs a number of representations of Lie groups via geometric quantization of coadjoint orbits. It appears that all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. The author successfully constructs Kählerian polarizations and real polarizations for elliptic and hyperbolic coadjoint orbits, respectively. Two classes of coadjoint orbits are quantized using these polarizations.