Computing Modular Data for Pointed Fusion Categories

Abstract

A formula for the modular data of \(\mathcal{Z}(Vec^{\omega}G)\) was given by Coste, Gannon and Ruelle in arXiv:arch-ive/0001158, but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra \(D^{\omega}G\). Further, we have written code to compute this modular data for many pairs of small finite groups and \(3\)-cocycles. This code is optimised using Galois symmetries of the \(S\) and \(T\) matrices. We have posted a database of modular data for the Drinfeld center of every Morita equivalence class of pointed fusion categories of dimension less than \(48\).