Automorphic Forms and Applications: Haowu Wang (LabEx CEMPI, University of Lille)

The Seminar Automorphic Forms and Applications will take place on Oct 30 at 18:00 in the room 306

Haowu Wang (LabEx CEMPI, University of Lille) will give a talk «Weyl invariant E₈ Jacobi forms 1»

Abstract: For the lattice constructed from the classical root system R, Wirthmuller defined Jacobi forms invariant under the Weyl group W(R). In 1992, Wirthmuller proved that the bigraded ring of W(R)-invariant weak Jacobi forms is a polynomial algebra over the ring of SL(2, Z) modular forms except the root system E₈. It is still an open problem how to extend the Wirthmuller's theorem to the case R=E₈. Weyl invariant E₈ Jacobi forms has applications in mathematics and physics, but very little has been known about its structure. In two talks, I will present an explicit description of the ring of W(E₈)-invariant Jacobi forms.
In this talk, I will first give a brief overview of Weyl invariant Jacobi forms and Wirthmuller's structure theorem. Then I will introduce a proper extension of Wirthmuller's theorem to the case of E₈ and show that the ring of W(E₈)-invariant weak Jacobi forms is not a polynomial algebra.