Quantum cohomology of G/P and homology of affine Grassmannian

@article{Lam2007QuantumCO,
  title={Quantum cohomology of G/P and homology of affine Grassmannian},
  author={Thomas Lam and Mark Shimozono},
  journal={Acta Mathematica},
  year={2007},
  volume={204},
  pages={49-90}
}
Let G be a simple and simply-connected complex algebraic group, P ⊂ G a parabolic subgroup. We prove an unpublished result of D. Peterson which states that the quantum cohomology QH*(G/P) of a flag variety is, up to localization, a quotient of the homology H*(GrG) of the affine Grassmannian GrG of G. As a consequence, all three-point genus-zero Gromov–Witten invariants of G/P are identified with homology Schubert structure constants of H*(GrG), establishing the equivalence of the quantum and… 
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