University of Sydney Algebra Seminar

Ying Xu (Hefei University of Technology)

Friday 2 September, 12-1pm, Place: Carslaw 375

Quantum correspondences of Lie superalgebras

A remarkable connection between osp(1|2n) and so(2n+1) was discovered in the early 80s, which can be understood in terms of an intriguing isomorphism between the quantised universal enveloping algebras of osp(1|2n) and so(2n+1). The same isomorphism emerged in very recent work of Mikhaylov and Witten on quantum Chern-Simons theories. Apart from their applications in superstring theory, quantum correspondences are beneficial for studying the representation theory of Lie superalgebras. We will describe a catalogue of the isomorphisms for families of pairs of quantum (affine) superalgebras, which are analogous to that between the quantum (super)groups of osp(1|2n) and so(2n+1), and show that the representation categories of the Hopf superalgebras in each pair are equivalent as strict tensor categories. This is joint work with Ruibin Zhang.