The structure of the algebra of weak Jacobi forms for the root system $F_4$

Abstract

We prove the polynomiality of the bigraded ring $J_{\ast ,\ast }^{w,W}(F_4)$ of weak Jacobi forms for the root system $F_4$ which are invariant with respect to the corresponding Weyl group. This work is a continuation of the joint article with V.A. Gritsenko, where the structure of algebras of the weak Jacobi forms related to the root systems of $D_n$ type for $2⩽n⩽8$ was studied.

19 pages

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