Affordable Access

$W(E_8)$-invariant Jacobi forms

Authors
  • Wang, Haowu
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.

Report this publication

Statistics

Seen <100 times