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Journal of Lie Theory 30 (2020), No. 4, 909--924
Copyright Heldermann Verlag 2020

Symplectic Level-Rank Duality via Tensor Categories

Victor Ostrik
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.

Michael Sun
no affiliation

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.

MSC: 18D10,17B67.

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