论文标题
上半平面和模块化形式的手性rham复合物
Chiral de Rham complex on the upper half plane and modular forms
论文作者
论文摘要
对于任何一致性亚组$γ$，我们研究了顶点操作员代数$ω^{ch}（\ mathbb h，γ）$由$γ$ incim-invariant全球段的全球整体组成，在上半平面上是所有cusps holomorphic the上半平面的。我们引入了$ sl（2，\ mathbb r）$ - 全球部分的不变过滤，并表明分级代数上的$γ$ invariants与模块化形式的某些副本同构。我们还给出了一个明确的公式，用于将模块化形式提升为$ω^{ch}（\ Mathbb H，γ）$，并计算$ω^{ch}的字符公式（\ Mathbb H，γ）$。此外，我们表明，顶点代数结构修改了兰金 - 孔支架，并且在涉及Eisenstein系列的恒定模块化形式之间，修饰的支架变为非零。
For any congruence subgroup $Γ$, we study the vertex operator algebra $Ω^{ch}(\mathbb H,Γ)$ constructed from the $Γ$-invariant global sections of the chiral de Rham complex on the upper half plane, which are holomorphic at all the cusps. We introduce an $SL(2,\mathbb R)$-invariant filtration on the global sections and show that the $Γ$-invariants on the graded algebra is isomorphic to certain copies of modular forms. We also give an explicit formula for the lifting of modular forms to $Ω^{ch}(\mathbb H,Γ)$ and compute the character formula of $Ω^{ch}(\mathbb H,Γ)$. Furthermore, we show that the vertex algebra structure modifies the Rankin-Cohen bracket, and the modified bracket becomes non-zero between constant modular forms involving the Eisenstein series.
