Braided Tensor Categories of Admissible Modules for Affine Lie Algebras - Creutzig, Thomas; Huang, Yi Zhi; Yang, Jinwei (Communications in Mathematical Physics, 2018)
Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We conjecture that this braided tensor category is rigid and thus is a ribbon category. We also give conjectures on the modularity of this category and on the equivalence with a suitable quantum group tensor category. In the special case that the affine Lie algebra is sl^ 2, we prove the rigidity and modularity conjectures.
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