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Vertex operator algebras, minimal models, and modular linear differential equations of order 4

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Nagatomo,  Kiyokazu
Max Planck Institute for Mathematics, Max Planck Society;

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Zagier,  Don
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Arike, Y., Nagatomo, K., & Sakai, Y. (2018). Vertex operator algebras, minimal models, and modular linear differential equations of order 4. Journal of the Mathematical Society of Japan, 70(4), 1347-1373. doi:10.2969/jmsj/74957495.


Cite as: http://hdl.handle.net/21.11116/0000-0003-C4EB-7
Abstract
In this paper we classify vertex operator algebras with three conditions which arise from Virasoro minimal models: (A) the central charge and conformal weights are rational numbers, (B) the space spanned by characters of all simple modules of a vertex operator algebra coincides with the space of solutions of a modular linear differential equation of order 4 and (C) the dimensions of first three weight subspaces of a VOA are 1, 0 and 1, respectively. It is shown that vertex operator algebras which we concern have central charges c= −46/3, −3/5, −114/7, 4/5, and are isomorphic to minimal models for c= −46/3, −3/5 and $Z_2$ -graded simple current extensions of minimal models for c= −114/7, 4/5.