Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor N of an RCFT and the quadratic residues modulo N play an important role in the computation and classification of Galois permutations. We establish a field correspondence in different theories through the picture of effective central charge, which combines Galois inner automorphisms and the structure of simple currents. We then make a first attempt to extend Hecke operators to the full data of modular tensor categories. The Galois symmetry encountered in the modular data transforms the fusion and the braiding matrices as well, and yields isomorphic structures in theories related by Hecke operators.

中文翻译：

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Hecke关系在有理共形场理论和相关模量张量类别中引起的Galois对称性

Hecke算子将有理共形场理论（RCFT）的特征与不同的中心电荷联系起来，并扩展了先前研究的模块化表示形式和融合代数的Galois对称性。我们表明，RCFT的导体N和模N的二次残基在Galois置换的计算和分类中起重要作用。我们通过有效中心电荷的图来建立不同理论中的场对应关系，该图结合了伽罗瓦内部自同构和简单电流的结构。然后，我们首先尝试将Hecke运算符扩展到模块化张量类别的完整数据。模块化数据中遇到的Galois对称性也转换了融合矩阵和编织矩阵，并在Hecke算子相关的理论中得出了同构结构。