We prove that the quantum cohomology ring of any minuscule orcominuscule homogeneous space, specialized at $q=1$, is semisimple.This implies that complex conjugation defines an algebra automorphismof the quantum cohomology ring localized at the quantumparameter. We check that this involution coincides with the strangeduality defined in our previous article. We deduce Vafa--Intriligator typeformulas for the Gromov--Witten invariants.
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