February 22

Deepak Naidu ( UNH )

Lagrangian subcategories of twisted quantum doubles of finite groups

Abstract: We will begin the talk by recalling the notion of a fusion category and related concepts. We will then present a classification of Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of arxiv:0704.0195v2 [math.QA] this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles of finite groups. We also establish a canonical bijection between Lagrangian subcategories of the representation category of a twisted quantum double of a finite group G and module categories over the category of twisted G-graded vector spaces such that the dual fusion category is pointed. As a consequence, we obtain that two group-theoretical fusion categories are weakly Morita equivalent if and only if their centers are equivalent as braided tensor categories.

This talk is based on a joint work with Dmitri Nikshych (Preprint: arXiv:0705.0665v1 [math.QA]).