Let K be a compact connected semisimple Lie group, let G be its complexifica- tion, and let G = KAN be an Iwasawa decomposition. Let T be the centralizer of A in K, so that H = TA is a Cartan subgroup of G. Since G and N are com- plex, G.N is a complex manifold. Besides the left G-action on G/N, there is also a right H-action because H normalizes N. In [10], Schwarz suggests the following scheme of geometric quantization on The space G/N: Equip G/N with a K-invariant Kahler structure w, and consider The corresponding prequantum line bundle L [6; 9].
展开▼
