Hans Wenzl, UC San Diego

Abstract: Module categories can be viewed as the analogue of subgroups for tensor categories. Indeed, all module categories of the category of representations of a finite group can be described in terms of its subgroups.  We study module categories of fusion categories coming from quantum groups at roots of unity. These can be classified via so-called modular invariants. We expect that for non-exceptional modular invariants, all of these module categories can be constructed via deformations of certain subgroups of the corresponding Lie group.  We present large classes of examples for which this has been checked.