ua nt - p h / 02 01 12 9 v 1 2 8 Ja n 20 02 Vector coherent state representations , induced representations , and geometric quantization : I . Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.