Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries

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.

17 pages

References in corpus (1)

• An Involution on the Quantum Cohomology Ring of the Grassmannian

Cited by in corpus (5)

• Semisimple quantum cohomology of some Fano varieties
• Quantum cohomology of G/P and homology of affine Grassmannian
• Positivity of minuscule quantum K-theory
• Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces
• An update of quantum cohomology of homogeneous varieties