Algebra Seminar: Xu -- Quantum correspondences of Lie superalgebras

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.