Slightly degenerate categories and $\mathbb{Z}$-modular data

Abstract

Given a slightly degenerate fusion category $\mathcal{C}$, we explain how it naturally gives rise to a Z-modular data. We do not restrict to spherical categories and work with pivotal categories instead. Finally, we give an interpretation in this framework of the Bonnafé-Rouquier categorification of the $\mathbb{Z}$-modular datum associated to non trivial family of the cyclic complex reflection group.

24 pages, added some examples, a theorem of Vafa and removed a mild hypothesis in section 3