Integral Metaplectic Modular Categories

Abstract

A braided fusion category is said to have Property $\text{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\text{F}$ by showing these categories are group theoretical. For the special case of integral categories $\mathcal{C}$ with the fusion rules of $SO(8{)}_2$ we determine the finite group $G$ for which $Rep(D^{\omega }G)$ is braided equivalent to $\mathcal{Z}(\mathcal{C})$. In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial at a point.

10 pages

References in corpus (1)

• Group-theoretical properties of nilpotent modular categories

Cited by in corpus (1)

• Quadratic $d$-numbers