On fractional level WZW models (non-integrable admissible affine Lie algebra irreps) for $\mathfrak{sl}(2, \mathbb{C})$:
Boris Feigin, Feodor Malikov, Modular functor and representation theory of $\widehat{\mathfrak{sl}_2}$ at a rational level, p. 357-405 in: Loday, Stasheff, Voronov (eds.) Operads: Proceedings of Renaissance Conferences, Contemporary Mathematics 202, AMS (1997) [arXiv:q-alg/9511011, ams:conm-202)]
(appearance of $\mathfrak{osp}(1\vert2)$-contributions)
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