论文标题
由一致亚组引起的简单顶点代数
Simple Vertex Algebras Arising From Congruence Subgroups
论文作者
论文摘要
Malikov等人引入的手性De Rham复合物。 1998年，在任何复杂的分析歧管或非符号代数品种上都是顶点代数的捆绑。从上半平面上全球de Rham复合体的全球部分的顶点代数开始，我们考虑了$γ$ incimormorormorormormormormormormormorphic in Cusps的子空间。该空间再次是一个顶点操作员代数，线性基础由Meromormormorphic模块化形式的提升公式组成。我们将描述两种类型的提升公式，并将Rankin-Cohen支架概括为Meromorormormormormormorphic模块化形式。作为一个应用程序，我们将证明由一致性子组构建的顶点代数很简单。
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.
