Affine $\mathfrak{sl}_2$ at admissible levels and quantum $\mathfrak{sl}_{2|1}$

Abstract

We prove braided tensor equivalences between the categories of weight modules of the affine vertex algebra of $\mathfrak{sl}_2$ at any admissible level and categories associated to partially semisimplified versions of quantum $\mathfrak{sl}_{2|1}$ at roots of unity.