Reflection fusion categories

Abstract

We introduce the notion of a $\text{reflection fusion category}$, which is a type of a $G$-crossed category generated by objects of Frobenius-Perron dimension $1$ and $\sqrt{p}$, where $p$ is an odd prime. We show that such categories correspond to orthogonal reflection groups over ${\mathbb{F}}_p$. This allows us to use the known classification of irreducible reflection groups over finite fields to classify irreducible reflection fusion categories.

27 pages: references to MR2674592 and arXiv:0005291 are added