Computing modular data for pointed fusion categories

Abstract

A formula for the modular data of Z(Vec G) was given by Coste, Gannon, and Ruelle in [9], but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra D 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 by taking advantage of 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 64. Show more