Duality for Jacobi Group Orbit Spaces and Elliptic Solutions of the WDVV Equations

From any given Frobenius manifold one may construct a so-called ’dual’ structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying the Witten– Dijkgraaf–Verlinde–Verlinde equations of associativity. Jacobi group orbit spaces naturally carry the structure of a Frobenius manifold and hence there exists a dual prepotential. In this paper this dual prepotential is constructed and expressed in terms of the elliptic polylogarithm function of Beilinson and Levin.