On Realizing Modular Data

TL;DR

This paper investigates the realization of certain modular data using advanced categorical techniques, identifying all possible realizations and linking them to quantum groups at roots of unity.

Contribution

It introduces a novel application of zesting and symmetry gauging to analyze modular data, revealing all realizations and their connections to quantum groups.

Findings

All realizations obtained from quantum groups at roots of unity.

Complete classification of realizations in one case.

Determined the form of possible realizations in another case.

Abstract

We use zesting and symmetry gauging of modular tensor categories to analyze some previously unrealized modular data obtained by Grossman and Izumi. In one case we find all realizations and in the other we determine the form of possible realizations; in both cases all realizations can be obtained from quantum groups at roots of unity.