Quantum correspondences of affine Lie superalgebras. (English) Zbl 1401.17009
Summary: There is a surprising isomorphism between the quantised universal enveloping algebras of \(\mathfrak{osp}(1 | 2n)\) and \(\mathfrak{so}(2n + 1)\). This same isomorphism emerged in recent work of V. Mikhaylov and E. Witten [Commun. Math. Phys. 340, No. 2, 699–832 (2015; Zbl 1326.81210)] in the context of string theory as a \(T\)-duality composed with an \(S\)-duality. We construct similar Hopf superalgebra isomorphisms for families of pairs of quantum affine superalgebras. An immediate consequence is that the representation categories of the quantum affine superalgebras in each pair are equivalent as strict tensor categories.
MSC:
17B20 | Simple, semisimple, reductive (super)algebras |
17B37 | Quantum groups (quantized enveloping algebras) and related deformations |