Symmetries of WDVV equations

We say that a function F(τ) obeys WDVV equations, if for a given invertible symmetric matrix ηαβ and all τ∈T⊂Rn, the expressions cβαγ(τ)=ηαλcλβγ(τ)=ηαλ∂λ∂β∂γF can be considered as structure constants of commutative associative algebra; the matrix ηαβ inverse to ηαβ determines an invariant scalar product on this algebra. A function xα(z,τ) obeying ∂α∂βxγ(z,τ)=z−1cαɛβ∂ɛxγ(z,τ) is called a calibration of a solution of WDVV equations. We show that there exists an infinite-dimensional group acting on the space of calibrated solutions of WDVV equations (in different form such a group was constructed in [A. Givental, math.AG/0305409]). We describe the action of Lie algebra of this group.