Frobenius manifold structure on orbit space of Jacobi groups; Part I

We give explicit formulae for the generators of the free polynomial algebra of Jacobi forms of type Al , Bl and G2 . With the aid of suitable generating functions we compute their intersection elements; this provides an elliptic deformation of analogous formulae for the polynomial invariants of Coxeter groups. The results are used in Part II to construct Frobenius manifold structures on the orbit spaces of the Jacobi groups of type Al and G2 .