2012/01/31 by Chongying Dong, Xingjun Lin, Siu-Hung Ng · 1 citation
Mathematics · Physics and Astronomy · #math.QA #hep-th #math-ph #math.CT #math.MP #math.RT #msc:17B69 #msc:18D10 #msc:20H05 #msc:81R05 #msc:81R50
paper · pdf · doi:10.2140/ant.2015.9.2121
published as Algebra & Number Theory, Vol. 9 (2015), No. 9, 2121-2166 · References are updated. Some typos and grammatical errors are corrected
arxiv created 2015/10/27 · arxiv updated 2015/11/10
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.