Reconstruction of tensor categories of type $G_2$

Abstract

We prove that any ribbon tensor category $\mathcal{C}$ with the fusion rules of the compact group of type $G_2$ is equivalent to the representation category of the corresponding Drinfeld-Jimbo quantum group for $q^2=1$ or $q^2$ not a root of unity. We also prove an analogous result for the corresponding ribbon fusion tensor categories at roots of unity.

arXiv comment42 pages