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.