I describe geometric quantization using a real polarization (as formulated by Jedrzej Sniatycki), and give a construction of geometric quantization of the moduli space of gauge equivalence classes of flat SU(2) connections on an oriented 2-manifold. I show that dimension of the physical Hilbert space in this quantization coincides with the dimension given by the Verlinde formula.

(Joint work with Jonathan Weitsman)

Reference: L. Jeffrey, J. Weitsman, Bohr-Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula, Commun. Math. Phys. 1992.