Braided tensor categories of admissible modules for affine Lie algebras

摘要

Using the tensor category theory developed by Lepowsky, Zhang and the secondauthor, we construct a braided tensor category structure with a twist on asemisimple category of modules for an affine Lie algebra at an admissiblelevel. We conjecture that this braided tensor category is rigid and thus is aribbon category. We also give conjectures on the modularity of this categoryand on the equivalence with a suitable quantum group tensor category. In thespecial case that the affine Lie algebra is $\widehat{\mathfrak{sl}}_2$, weprove the rigidity and modularity conjectures.