2019/06/30 by Pinhas Grossman, Masaki Izumi
Mathematics · #math.OA #math.QA #msc:46L37 #msc:18D10
paper · pdf · doi:10.1007/s00220-020-03710-7
Corrected typos and other minor editing; mathematica notebook added; appendix merged with main article (the body is the 59 pages)
arxiv created 2019/09/11 · arxiv updated 2020/12/02
We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with some conditions on the fixed points of the involutions and the relative sizes of the groups. From this input we construct S and T matrices which satisfy the modular relations and whose Verlinde coefficients are non-negative integers. We also check certain restrictions coming from Frobenius-Schur indicators. These families generalize Evans and Gannon's conjectures for the modular data associated to generalized Haagerup and near-group categories for odd groups, and include the modular data of the Drinfeld centers of almost all known quadratic categories. In addition to the subfamilies which are conjecturally realized by centers of quadratic categories, these families include many examples of potential modular data which do not correspond to known types of modular tensor categories.