Berezin-Toeplitz Quantization of the Moduli Space of Flat $\mathrm{SU}(N)$ Connections

Abstract

The moduli space of flat $\mathrm{SU}(n)$ connections on Riemann surfaces is of fundamental importance in TQFT. There is an associated representation of the mapping class group on the space of covariantly constant sections of the Verlinde bundle with respect to the AdPW-H connection. J. Andersen showed that this representation is asymptotically faithful. In his proof the Berezin-Toeplitz quantization of compact Kähler manifolds is used. In this contribution the background and some ideas of Andersen's proof is sketched.