Braided tensor categories of admissible modules for affine Lie algebras

Abstract

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 ${\widehat{\mathfrak{sl}}}_2$, we prove the rigidity and modularity conjectures.

arXiv commentComments are welcome

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