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Level bounds for exceptional quantum subgroups in rank two

    There is a long-standing belief that the modular tensor categories 𝒞(𝔤,k), for k1 and finite-dimensional simple complex Lie algebras 𝔤, contain exceptional connected étale algebras (sometimes called quantum subgroups) at only finitely many levels k. This premise has known implications for the study of relations in the Witt group of nondegenerate braided fusion categories, modular invariants of conformal field theories, and the classification of subfactors in the theory of von Neumann algebras. Here, we confirm this conjecture when 𝔤 has rank 2, contributing proofs and explicit bounds when 𝔤 is of type B2 or G2, adding to the previously known positive results for types A1 and A2.

    AMSC: 81R50

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