Document Type
Article
Publication Date
1-1-2015
Abstract
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of any rational, C2-cofinite vertex operator algebra is a congruence subgroup. In particular, the q-character of each irreducible module is a modular function on the same congruence subgroup. The Galois symmetry of the modular representations is obtained and the order of the anomaly for those modular categories satisfying some integrality conditions is determined.
Publication Source (Journal or Book title)
Algebra and Number Theory
First Page
2121
Last Page
2166
Recommended Citation
Dong, C., Lin, X., & Ng, S. (2015). Congruence property in conformal field theory. Algebra and Number Theory, 9 (9), 2121-2166. https://doi.org/10.2140/ant.2015.9.2121