Abstract:
In 1992, Wirthmüller proved that for the lattice constructed from a
classical root system (except E_8), the corresponding space of Jacobi
forms which are invariant under the Weyl group is a polynomial algebra
over the ring of modular forms. In the talk we will focus on
discussing the remaining case E_8. We will show that the space of
Weyl invariant E_8 Jacobi forms is not a polynomial algebra and
present a proper extension of Wirthmüller's theorem in the case. We
will also give the generators of indices 2, 3, 4.
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