Reconstruction of Modular Data from SL_2(ℤ) Representations

Communications in Mathematical Physics(2023)

引用 0|浏览0
暂无评分
摘要
Modular data is a 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(ℤ/ n ℤ) . We discover and collect many conditions on the SL_2(ℤ/ n 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(ℤ/ n 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 of modular data, up to Galois conjugation and changing spherical structure. 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. Our classification employs a hybrid of automated computational methods and by-hand calculations.
更多
查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要