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

Abel Lacabanne (1)

1 UCL IRMP - Institut de Recherche en Mathématiques et Physique

Given a slightly degenerate fusion category $\mathcal{C}$, we explain how it naturally gives rise to a $\mathbb{Z}$-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.

Domaines: Algèbres quantiques [math.QA]; Catégories et ensembles [math.CT]

Abel Lacabanne. Slightly degenerate categories and $\mathbb{Z}$-modular data. International Mathematics Research Notices, 2019, 2021 (Issue 12), pp. 9340-9374. ⟨10.1093/imrn/rnz105⟩. ⟨hal-01827846v3⟩