Geometric Quantization on a Coset Space G/H

Abstract

Geometric quantization on a coset space $G/H$ is considered, intending to recover Mackey's inequivalent quantizations. It is found that the inequivalent quantizations can be obtained by adopting the symplectic 2-form which leads to Wong's equation. The irreducible representations of $H$ which label the inequivalent quantizations arise from Weil's theorem, which ensures a Hermitian bundle over $G/H$ to exist.