Claremont Topology Seminar: Qing Zhang (UC Santa Barbara)

Title: Super-modular categories from near-group centers

Abstract: A super-modular category is a unitary pre-modular category with Müger center equivalent to the symmetric unitary category of super-vector spaces. The modular data for a super-modular category gives a projective representation of the group:  $\Gamma_\theta<\mathrm{SL}(2, \mathbb{Z})$. Adapting work of Ng-Rowell-Wang-Wen, Cho- Kim-Seo-You computed modular data from congruence representations of $\Gamma_\theta $ using the congruence subgroup theorem for super-modular categories of  Bonderson-Rowell-Wang-Z and the minimal modular extension theorem of  Reutter-Johnson-Freyd. They found two classes of previously unknown modular data for rank 10 super-modular categories. We show that these data are realized by modifying the Drinfeld centers of near-group fusion categories associated with the groups $\Z/6$ and $\Z/2\times \Z/4$. The methods we develop have more general applications, and we describe some of them. This talk is based on joint work with Eric Rowell and Hannah Solomon.