Mathematical Research Letters

Volume 25 (2018)

Number 3

Quantum correspondences of affine Lie superalgebras

Pages: 1009 – 1036



Ying Xu (School of Mathematics, Hefei University of Technology, Anhui Province, China)

R. B. Zhang (School of Mathematics and Statistics, University of Sydney, NSW, Australia)


There is a surprising isomorphism between the quantised universal enveloping algebras of $\mathfrak{osp}(1 \vert 2n)$ and $\mathfrak{so}(2n + 1)$. This same isomorphism emerged in recent work of Mikhaylov and Witten 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.

Received 7 November 2016

Accepted 21 April 2017

Published 3 August 2018