Simple Vertex Algebras Arising From Congruence Subgroups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913468800565248 |
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| author | Dai, Xuanzhong Song, Bailin |
| author_facet | Dai, Xuanzhong Song, Bailin |
| contents | 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 $Γ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10090 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simple Vertex Algebras Arising From Congruence Subgroups Dai, Xuanzhong Song, Bailin Quantum Algebra Representation Theory 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 $Γ$-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. |
| title | Simple Vertex Algebras Arising From Congruence Subgroups |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2211.10090 |