Bohr-Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula (Q1208015)

The prequantum system given by the moduli space of flat \(SU(2)\) connections on a two-dimensional manifold \(\Sigma^ g\) of genus \(g\) is quantized in a suitable real polarization associated to a trinion decomposition of the two-manifold. The number of Bohr-Sommerfeld orbits of this quantization is shown to equal the Verlinde dimension, and therefore to match the dimension of the Hilbert space arising from a Kähler polarization.