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 condensation of the Drinfeld center of the near-group category $\mathbb{Z}/4\mathbb{Z}\times \mathbb{Z}/4\mathbb{Z}+16$, and 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 the non-pointed factor of its condensation has the same modular data as the quantum group category $C({\mathfrak{g}}_2,4)$.

30 pages. Added Proposition 3.9 and Remark 3.10. Fixed minor typos