论文标题
Weyl不变的Jacobi形式：一种新方法
Weyl invariant Jacobi forms: a new approach
论文作者
论文摘要
与正定晶格相关的积分重量和积分指数的弱雅各比形式形成了一个大代数。在本文中，我们证明了这种代数是免费的标准。作为应用程序，我们给出了K.wirthmüller定理的自动形态证明，该定理断言弱雅各比的大代数在韦伊尔组下不变是任何不可修复的根系，而不是$ e_8 $的类型的多项式代数。此方法也适用于$ e_8 $。即使已知$ e_8 $ jacobi表单的代数是非免费的，我们仍然得出一个新的结构结果。
The weak Jacobi forms of integral weight and integral index associated to an even positive definite lattice form a bigraded algebra. In this paper we prove a criterion for this type of algebra being free. As an application, we give an automorphic proof of K. Wirthmüller's theorem which asserts that the bigraded algebra of weak Jacobi forms invariant under the Weyl group is a polynomial algebra for any irreducible root system not of type $E_8$. This approach is also applicable to $E_8$. Even if the algebra of $E_8$ Jacobi forms is known to be non-free, we still derive a new structure result.
