On the Duflo Formula for L∞-algebras and Q-manifolds

We prove a direct analogue of the classical Duflo formula in the case of L∞algebras. We conjecture an analogous formula in the case of an arbitrary Q-manifold. When G is a compact connected Lie group, the Duflo theorem for the Q-manifold (ΠTG, dDR) is exactly the Duflo theorem for the Lie algebra g = LieG. The corresponding theorem for the Q-manifold (ΠTM,dDR), where M is an arbitrary smooth manifold, is a generalization of the Duflo theorem for the case of smooth manifolds. On the other hand, the Duflo theorem for the Q-manifold (ΠT holM, ∂), where M is a complex manifold, is a generalization of the M.Kontsevich’s “theorem on complex manifold” [K1], Sect. 8.4.