Journal of Lie Theory 30 (2020), No. 4, 909--924
Copyright Heldermann Verlag 2020
Symplectic Level-Rank Duality via Tensor Categories
Dept. of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A.;
and: Laboratory of Algebraic Geometry, National Research University, Higher School of Economics, Moscow, Russia
Eric C. Rowell
Dept. of Mathematics, Texas & University, College Station, TX 77843-3368, U.S.A.
We give two proofs of a level-rank duality for braided fusion categories obtained from quantum groups of type C at roots of unity. The first proof uses conformal embeddings, while the second uses a classification of braided fusion categories associated with quantum groups of type C at roots of unity. In addition we give a similar result for non-unitary braided fusion categories quantum groups of types B and C at odd roots of unity.
Keywords: Braided fusion category, affine Lie algebra, level-rank duality.
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