MINIMAL REPRESENTATIONS, GEOMETRIC-QUANTIZATION, AND UNITARITY

In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pi(o) of every simply-connected real Lie group G(o) such that the maximal compact subgroup of G(o) has finite center and G(o) admits some minimal representation. We obtain algebraic and analytic results about pi(o). We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then ''quantize'' these results to obtain the corresponding representations. We assume (Lie C-o)(C) is simple.