We introduce the notion of a $\textit{ reflection fusion category}$, 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.
Categories: math.QA