Abstract
We compute the monoidal and braided auto-equivalences of the modular tensor categories C(slr+1,k), C(so2r+1,k), C(sp2r,k), and C(g2,k). Along with the expected simple current auto-equivalences, we show the existence of the charge conjugation auto-equivalence of C(slr+1,k), and exceptional auto-equivalences of C(so2r+1,2), C(sp2r,r), C(g2,4). We end the paper with a section discussing potential applications of these computations, including the relationship of these computations to the program to classify quantum subgroups of the simple Lie algebras. Included is an appendix by Terry Gannon, which discusses the group structure of the auto-equivalences of C(slr+1,k).
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