  We compute the monoidal and braided auto-equivalences of the modular tensor
categories $\mathcal{C}(\mathfrak{sl}_{r+1},k)$,
$\mathcal{C}(\mathfrak{so}_{2r+1},k)$, $\mathcal{C}(\mathfrak{sp}_{2r},k)$, and
$\mathcal{C}(\mathfrak{g}_{2},k)$. Along with the expected simple current
auto-equivalences, we show the existence of the charge conjugation
auto-equivalence of $\mathcal{C}(\mathfrak{sl}_{r+1},k)$, and exceptional
auto-equivalences of $\mathcal{C}(\mathfrak{so}_{2r+1},2)$,
$\mathcal{C}(\mathfrak{sp}_{2r},r)$, $\mathcal{C}(\mathfrak{g}_{2},4)$. We end
the paper with a section discussing potential applications of these
computations.
