Congruence property in orbifold theory
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Abstract:
Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated to $V$ and $G$ is a congruence subgroup. In particular, the $q$-character of each irreducible twisted module is a modular function on the same congruence subgroup. In the case $V$ is the Frenkel-Lepowsky-Meurman’s moonshine vertex operator algebra and $G$ is the monster simple group, the generalized McKay-Thompson series associated to any commuting pair in the monster group is a modular function.References
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Additional Information
- Chongying Dong
- Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
- MR Author ID: 316207
- Li Ren
- Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China
- MR Author ID: 904508
- Received by editor(s): October 17, 2016
- Received by editor(s) in revised form: March 27, 2017
- Published electronically: August 31, 2017
- Additional Notes: The first author was supported by a NSF grant DMS-1404741 and China NSF grant 11371261
The second author was supported by China NSF grant 11301356 - Communicated by: Kailash C. Misra
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 497-506
- MSC (2010): Primary 17B69
- DOI: https://doi.org/10.1090/proc/13748
- MathSciNet review: 3731686