Modular Categories of Dimension $p^{3}m$ with $m$ Square-Free

Abstract

We give a complete classification of modular categories of dimension $p^{3}m$ where $p$ is prime and $m$ is a square-free integer. When $p$ is odd, all such categories are pointed. For $p=2$ one encounters modular categories with the same fusion ring as orthogonal quantum groups at certain roots of unity, namely $SO(2m{)}_2$. As an immediate step we classify a more general class of so-called even metaplectic modular categories with the same fusion rules as $SO(2N{)}_2$ with $N$ odd.

arXiv commentVersion 2: typos corrected Version 3: several proofs tightened up, typos corrected and improvement of exposition