Rigidity of $\mathbf{SU(2)}$ and $\mathbf{SO(3)}$ quantum representations of mapping class groups at prime levels

Abstract

We prove the rigidity of Witten-Reshetikhin-Turaev $\mathrm{SU}(2)$ and $\mathrm{SO}(3)$ quantum representations of mapping class groups at all prime levels for closed surfaces of genus at least $7$. The proof relies on Ocneanu rigidity of modular categories and harmonic representatives in Hodge theory.