Speaker
Kaiwen Sun
(KIAS)
Description
In 1992 Wirthmuller showed that for any root system of type A,B,C,D,G,F and E6,E7, the ring of weak Jacobi forms invariant under Weyl group is a polynomial algebra. However, it has recently been proved that for E8 the ring is not a polynomial algebra. I will present how to describe E8 Weyl invariant Jacobi forms properly, both weak and holomorphic, and also how to used them in the modular bootstrap of elliptic genera of E-strings. For example, we prove that for any Weyl invariant E8 Jacobi form \phi_t of index t the function E4^[t/5]\Delta^[5t/6]\phi_t can be expressed uniquely as a polynomial in E4, E6 and Sakai's nine Ai, Bj forms. This is based on a joint work with Haowu Wang arXiv:2109.10578.
