On the Dubrovin Connection for G/b

We show that the small quantum product of the generalized flag manifold G/B is a product operation on H * (G/B) ⊗ R[q 1 ,. .. , q l ] uniquely determined by the fact that it is a deformation of the cup product on H * (G/B), it is commutative, associative, graded with respect to deg(q i) = 4, it satisfies a certain relation (of degree two), and the corresponding Dubrovin connection is flat. We deduce that it is again the flatness of the Dubrovin connection which characterizes essentially the solutions of the " quantum Giambelli problem " for G/B (this fact was suggested by Guest [Gu]). We are also able to deduce a new proof of the quantum Chevalley formula (see D. Peterson [Pe], and Fulton and Woodward [Fu-Wo]).