Invariant measures on polarized submanifolds in group quantization

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group R+ allows us to restore the strict invariance of the measures and, accordingly, the unitarity of the quantization of coadjoint orbits. As an example, the representations of SL(2,ℝ) are recovered. © 2000 American Institute of Physics.