SMS scnews item created by Kevin Coulembier at Fri 19 Aug 2016 1132
Type: Seminar
Modified: Sun 21 Aug 2016 1524
Distribution: World
Expiry: 30 Sep 2016
Calendar1: 2 Sep 2016 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Quantum correspondences of Lie superalgebras
Auth: kevinc@pkevinc.pc (assumed)

# 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.


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