# Modular invariance of characters of vertex operator algebras

@article{Zhu1995ModularIO, title={Modular invariance of characters of vertex operator algebras}, author={Yongchang Zhu}, journal={Journal of the American Mathematical Society}, year={1995}, volume={9}, pages={237-302} }

In contrast with the finite dimensional case, one of the distinguished features in the theory of infinite dimensional Lie algebras is the modular invariance of the characters of certain representations. It is known [Fr], [KP] that for a given affine Lie algebra, the linear space spanned by the characters of the integrable highest weight modules with a fixed level is invariant under the usual action of the modular group SL2(Z). The similar result for the minimal series of the Virasoro algebra is…

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