On near-group centers and super-modular categories
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abstract
The construction and classification of super-modular categories is an ongoing project, of interest in algebra, topology and physics. In a recent paper, Cho, Kim, Seo and You produced two mysterious families of super-modular data, with no known realization. We show that these data are realized by modifying the Drinfeld centers of near-group fusion categories associated with the groups $mathbb Z/6$ and $mathbb Z/2 imes mathbb Z/4$. The methods we develop have wider applications and we describe some of these, with a view towards understanding when near-group centers provide super-modular categories.