Reflection fusion categories


We introduce the notion of a 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.

J. Algebra 516 (2018), 172–196