A general quintic hypersurface in CP 4 is a compact Calabi-Yau threefold. Its rational Gromov-Witten invariants have been predicted by mirror symmetry discovered in string theory [1]. The prediction proved by Givental [7] is to be explained as follows. Let n d be the virtual number of degree d rational curves in the quintic threefold and let F(q) =. The Givental J-function J for the quintic hypersurface satisfies the so-called quantum differential equation Equivariant Mirrors 861 every b β depends on e ±t 0 . So, [∆, α 0 =k a α ∂ α ] has no order m + 1 part. Now we apply the induction hypothesis to α 0 =k a α ∂ α whose coefficients do not depend on t 0 and conclude that a α ∈ C[h] if α 0 = k. The conclusion is contradictory to the assumption that for all α, a α is not in C[h]. Theorem 2.2. The operators D i , i = 1, . . . , n + 1, commute. Proof. The commutativity of H and D i is proven in [8]. Since [H, [D i , D j ]] = 0, by Proposition 2.1, the highest order part of [D i , D j ] has coefficients in C[h]. Now it is enough to prove the following claim. For any multi-indices α and β and any a and b in the polynomial ring C[h, q 1 , . . . , q n ], if we let [a∂ α , b∂ β ] = c γ ∂ γ , then any c γ cannot be in C[h]