# 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 We prove an unpublished result of D. Peterson which states that the quantum cohomology QH*(G/P) of a flag variety is, up to localization, a quotient of the homology H*(GrG) of the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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