The non-semisimple Kazhdan-Lusztig category for affine ${\mathfrak{sl}}_2$ at admissible levels

Robert McRae, Jinwei Yang

We show that Kazhdan and Lusztig's category $K{L}^k({\mathfrak{sl}}_2)$ of modules for the affine Lie algebra ${\widehat{\mathfrak{sl}}}_2$ at an admissible level $k$, equivalently the c…