Weyl不变Jacobi型：一种新的方法
Weyl invariant Jacobi forms: a new approach
摘要：
偶正定格的积分权和积分指数的弱Jacobi形式构成一个双阶化代数。本文证明了这类代数是自由代数的一个判据。作为应用，我们给出了K的一个自守证明。Wirthmüller定理，它断言弱Jacobi形式不变的双阶代数在外尔群下是多项式代数，对于任何非$E_8$型的不可约根系。该方法也适用于$E_8$。即使已知$E_8$ Jacobi形式的代数是非自由的，我们仍然得到了一个新的结构结果。
英文摘要：
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.
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