Norm estimates and asymptotic faithfulness of the quantum SU(n) representations of the mapping class group

Journal article, 2020

We give a direct proof for the asymptotic faithfulness of the quantum SU(n) representations of the mapping class group using peak sections in Kodaira embedding. We give also estimates on the norm of the parallell transport of the projective connection on the Verlinde bundle. The faithfulness has been proved earlier by J. E. Andersen using Toeplitz operators on compact Kähler manifolds and by J. Marché and M. Narimannejad using skein theory.