与二次范畴有关的潜在模数据的无限族
Infinite families of potential modular data related to quadratic categories
摘要：
我们提出了几个无限家庭的潜在模块化数据的Drinfeld中心的二次类的例子。在每种情况下，输入是一对高斯和相差一个符号的对合度量群，以及对合的不动点和群的相对大小的一些条件。从这个输入，我们构造$S$和$T$矩阵，满足模关系，其Verlinde系数是非负整数。我们还检查了来自Frobenius-Schur指标的某些限制。这些族推广了埃文斯和甘农的代数，用于与广义Haagerup和奇数群的近群范畴相关的模数据，并包括几乎所有已知二次范畴的德林费尔德中心的模数据。除了通过二次范畴的中心来实现的子族之外，这些族还包括许多不对应于已知类型的模张量范畴的潜在模数据的例子。
英文摘要：
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.
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