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arXiv · 2211.10090

Simple Vertex Algebras Arising From Congruence Subgroups

Xuanzhong Dai·Bailin Song
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Abstract

Chiral de Rham complex introduced by Malikov et al. in 1998, is a sheaf of vertex algebras on any complex analytic manifold or non-singular algebraic variety. Starting from the vertex algebra of global sections of chiral de Rham complex on the upper half plane, we consider the subspace of $\Gamma$-invariant sections that are meromorphic at the cusps. The space is again a vertex operator algebra, with a linear basis consisting of lifting formulas of meromorphic modular forms. We will describe two types of lifting formulas, and generalize the Rankin-Cohen bracket to the meromorphic modular forms. As an application, we will show that the vertex algebras constructed by congruence subgroups are simple.

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BibTeXRIS

Xuanzhong Dai, Bailin Song. 2022-11-18. Simple Vertex Algebras Arising From Congruence Subgroups. https://arxiv.org/abs/2211.10090

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