Asymptotic Faithfulness of Quantum $\mathrm{Sp}(4)$ Mapping Class Group Representations

Abstract

We prove asymptotic faithfulness for the quantum Sp(4) mapping class group representation. This provides the first example of asymptotic faithfulness lying outside of the A n family. The methods used are generalized from the proof of asymptotic faithfulness for skein SU (2) k mapping class group representations. In short, for any noncentral mapping class a comparison vector is found which allows for the mapping class to be detected.