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# Mathematical Research Letters

## Volume 25 (2018)

### Number 3

### Quantum correspondences of affine Lie superalgebras

Pages: 1009 – 1036

DOI: http://dx.doi.org/10.4310/MRL.2018.v25.n3.a14

#### Authors

#### Abstract

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