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