Quantum cohomology of G/P and homology of affine Grassmannian

@article{Lam2007QuantumCO,
  title={Quantum cohomology of G/P and homology of affine Grassmannian},
  author={Tony K.T. 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 We prove an unpublished result of D. Peterson which states that the quantum cohomology QH*(G/P) of a flag variety is, up to localization, a quotient of the homology H*(GrG) of the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… CONTINUE READING
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Peterson’s comparison theorem for Gromov-Witten invariants

D. C. Woodward On
  • Proc. Amer. Math. Soc
  • 2005
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

and H

A. Buch, A. Kresch
  • Tamvakis: Gromov-Witten invariants on Grassmannians, J. Amer. Math. Soc. 16
  • 2003
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

and I

R. Bezrukavnikov, M. Finkelberg
  • Mirković: Equivariant homology and Ktheory of affine Grassmannians and Toda lattices, Compos. Math. 141
  • 2005
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

and J

L. Lapointe, A. Lascoux
  • Morse: Tableau atoms and a new Macdonald positivity conjecture, Duke Math J. 116/1
  • 2004
VIEW 13 EXCERPTS
HIGHLY INFLUENTIAL

Quantum cohomology of flag varieties

VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL