@article{Operators:2323,
      recid = {2323},
      author = {Wu, Yuxiao},
      title = {Hecke Operators and Galois Symmetry in Rational Conformal  Field Theory},
      publisher = {University of Chicago},
      school = {Ph.D.},
      address = {2020-06},
      pages = {158},
      abstract = {We define Hecke operators on vector-valued modular forms  of the type that appear as characters of rational conformal  field theories (RCFTs). We apply our results to derive a  number of relations between characters of known RCFTs with  different central charges, and extend the previously stud-  ied Galois symmetry of modular representations and fusion  algebras. We show that the conductor N of a 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 trans- forms the fusion and the braiding matrices as  well, and yields isomorphic structures in theories related  by Hecke operators.},
      url = {http://knowledge.uchicago.edu/record/2323},
      doi = {https://doi.org/10.6082/uchicago.2323},
}