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Consider a physical system for which a mathematically rigorous geometricquantization procedure exists. Now subject the system to a finite set ofirreducible first class (bosonic) constraints. It is shown that there is amathematically rigorous BRST quantization of the constrained system whosecohomology at ghost number zero recovers the constrained quantum states.Moreover this space of constrained states has a well-defined Hilbert spacestructure inherited from that of the original system. Treatments of these ideasin the Physics literature are more general but suffer from having states withinfinite or zero "norms" and thus are not admissible as states. Also the BRSToperator for many systems require regularization to be well-defined. In ourmore restricted context we show that our treatment does not suffer from any ofthese difficulties. This work was submitted for publication March 21,2006

BRST Extension of Geometric Quantization