Irreducibility of quantum representations of mapping class groups with boundary

We prove that the Witten–Reshetikhin–Turaev $\mathrm{S}\mathrm{U}(2)$ quantum representations of mapping class groups are always irreducible in the case of surfaces equipped with colored banded points, provided that at least one banded point is colored by one. We thus generalize a well–known result due to J. Roberts.