论文标题
正交模块形式的自由代数分类
The classification of free algebras of orthogonal modular forms
论文作者
论文摘要
我们证明，在IV型对称域上的自动形式的分级代数是自由的，这是一个必要且充分的条件。根据必要的条件，我们得出分类结果。令$ m $是签名$（2，n）$拆分两架双曲机飞机的偶数格子。假设$γ$是包含判别内核的$ m $积分正交组的子组。事实证明，恰好有26个组$γ$，因此$γ$的模块化表格空间是免费的代数。使用足够的条件，我们恢复了一些众所周知的结果。
We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV to be free. From the necessary condition, we derive a classification result. Let $M$ be an even lattice of signature $(2,n)$ splitting two hyperbolic planes. Suppose $Γ$ is a subgroup of the integral orthogonal group of $M$ containing the discriminant kernel. It is proved that there are exactly 26 groups $Γ$ such that the space of modular forms for $Γ$ is a free algebra. Using the sufficient condition, we recover some well-known results.
