  We prove that the quantum cohomology ring of any minuscule or cominuscule
homogeneous space, specialized at q=1, is semisimple. This implies that complex
conjugation defines an algebra automorphism of the quantum cohomology ring
localized at the quantum parameter. We check that this involution coincides
with the strange duality defined in a previous paper. We deduce
Vafa-Intriligator type formulas for the Gromov-Witten invariants.
