Invariant Measures on Polarized Submanifolds in Group Quantization

Abstract

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 $SL(2,\Real)$ are recovered.