# $W(E_8)$-invariant Jacobi forms

- Authors
- Publication Date
- Feb 21, 2018
- Source
- Kaleidoscope Open Archive
- Keywords
- Language
- English
- License
- Unknown
- External links

## Abstract

We investigate Jacobi forms invariant under the action of the Weyl group of root lattice $E_8$. Such Jacobi forms are called $W(E_8)$-invariant Jacobi forms. We prove that every $W(E_8)$-invariant Jacobi form can be expressed uniquely as a polynomial in nine algebraically independent holomorphic Jacobi forms introduced by Sakai with coefficients which are meromorphic modular forms. The space of $W(E_8)$-invariant weak Jacobi forms of fixed index is a free module over the ring of modular forms. When index is less than $5$, we determine the structure of the corresponding module and construct all generators.