2011-02-04

Meng-Kiat Chuah, National Tsing Hua University in Taiwan

Models of semisimple Lie groups

Let G be a real semisimple Lie group. We consider certain fibrations over its integral elliptic or hyperbolic coadjoint orbits, equipped with G-invariant symplectic forms. Geometric quantization leads to unitary G-representations on Hilbert spaces. They consist of families of discrete series or principal series, whose occurrences depend on the image of the moment map. We also show that quantization commutes with reduction.