XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Martin Schlichenmaier

Berezin-Toeplitz quantization of the moduli space of flat SU(N) connections

As was shown by Bordemann, Meinrenken, and Schlichenmaier the Berezin-Toeplitz operator quantization and its associated star product give a unique natural quantization for a quantisable compact Kaehler manifold. This procedure is applied for the moduli space of gauge equivalence classes of SU(N) connections on a fixed Riemann surface. In this context the Verlinde spaces and the Verlinde bundle over Teichmueller space show up. Recent results of J. Andersen on the asymptotic faithfulness of the representation of the mapping class group on the space of covariantly constant sections of the Verlinde bundle are presented.