Equivariant prequantization and the moment map

Abstract

If ω is a closed G-invariant 2-form and μ a moment map, then we obtain necessary and sufficient conditions for equivariant pre-quantizability that can be computed in terms of the moment map μ. We also compute the obstructions to lift the action of G to a pre-quantization bundle of ω. Our results are valid for any compact and connected Lie group G.