Braided tensor categories of admissible modules for affine Lie algebras

Understand

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.