Congruence property in orbifold theory

Dong, Chongying; Ren, Li

doi:10.1090/proc/13748

Congruence property in orbifold theory
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by Chongying Dong and Li Ren PDF

Proc. Amer. Math. Soc. 146 (2018), 497-506 Request permission

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.

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