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.

66 pages