Realizing Modular Data from Centers of Near-group Categories

Abstract

In this paper, we show the existence of a near-group category of type \(\mathbb {Z} / 4\mathbb {Z} \times \mathbb {Z} / 4\mathbb {Z}+16\) and compute the modular data of its Drinfeld center. We prove that a modular data of rank 10 can be obtained through a condensation of the Drinfeld center of the near-group category \(\mathbb {Z} / 4\mathbb {Z} \times \mathbb {Z} / 4\mathbb {Z}+16\), and that it can also be realized as the Drinfeld center of a fusion category of rank 4. Moreover, we compute the modular data for the Drinfeld center of a near-group category \(\mathbb {Z} / 8\mathbb {Z}+8\) and show that, up to Galois conjugation, the non-pointed factor of its condensation has the same modular data as the quantum group category \(\mathcal {C}(\mathfrak {g}_2, 4)\).