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Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries

Pierre-Emmanuel Chaput·Laurent Manivel·Nicolas Perrin
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Abstract

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated as a strange duality property for the Gromov-Witten invariants, which turn out to be very symmetric.

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Pierre-Emmanuel Chaput, Laurent Manivel, Nicolas Perrin. 2006-09-28. Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries. https://doi.org/10.1093/imrn%2Frnm107

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