论文标题
从$ sl_2（\ mathbb {z}）$表示的模块化数据重建
Reconstruction of modular data from $SL_2(\mathbb{Z})$ representations
论文作者
论文摘要
模块化数据是模块化张量类别中最重要的不变性。我们通过直接从$ sl_2（\ Mathbb {z}/n \ mathbb {z}）$的不可缩放表示形式直接构建模块化$ s $和$ t $矩阵来追求模块化张量类别模块数据的方法。我们在$ SL_2（\ Mathbb {Z}/N \ Mathbb {Z}）$表示上发现并收集许多条件，以识别与某些模块化数据相对应的那些。为了从表示形式到达具体矩阵，我们还开发了使我们可以选择$ sl_2（\ Mathbb {z}/n \ mathbb {z}）$表示的适当基础的方法，以便它们具有模块化数据的形式。我们将此技术应用于等级的分类-6 $模块化张量类别，并获得模块化数据的分类。大多数计算可以使用计算机代数系统自动化，该系统可用于对高级模块化张量类别的模块化数据进行分类。
Modular data is the most significant invariant of a modular tensor category. We pursue an approach to the classification of modular data of modular tensor categories by building the modular $S$ and $T$ matrices directly from irreducible representations of $SL_2(\mathbb{Z}/n \mathbb{Z})$. We discover and collect many conditions on the $SL_2(\mathbb{Z}/n \mathbb{Z})$ representations to identify those that correspond to some modular data. To arrive at concrete matrices from representations, we also develop methods that allow us to select the proper basis of the $SL_2(\mathbb{Z}/n \mathbb{Z})$ representations so that they have the form of modular data. We apply this technique to the classification of rank-$6$ modular tensor categories, obtaining a classification up to modular data. Most of the calculations can be automated using a computer algebraic system, which can be employed to classify modular data of higher rank modular tensor categories.
