Abstract
A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given. As an application, it is shown that the characters of some modules of an intermediate vertex subalgebra between E 7 and E 8 lattice vertex operator algebras satisfy some modular differential equations. This result is an analogue of the result concerning the “hole” of the Deligne dimension formulas and the intermediate Lie algebra between the simple Lie algebras E 7 and E 8.
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After finishing this work, we learned of a recent related work by Kaneko et al. [20], where the Kaneko–Zagier equations and the Mathur–Mukhi–Sen classification are studied in detail.
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Kawasetsu, K. The Intermediate Vertex Subalgebras of the Lattice Vertex Operator Algebras. Lett Math Phys 104, 157–178 (2014). https://doi.org/10.1007/s11005-013-0658-x
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DOI: https://doi.org/10.1007/s11005-013-0658-x