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arXiv · 2007.16033

Weyl invariant Jacobi forms: a new approach

Haowu Wang
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Abstract

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. Wirthm\"{u}ller'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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Haowu Wang. 2020-07-31. Weyl invariant Jacobi forms: a new approach. https://doi.org/10.1016/j.aim.2021.107752

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