K -theory Schubert calculus of the affine Grassmannian

@article{Lam2010KS,
  title={K -theory Schubert calculus of the affine Grassmannian},
  author={Thomas Lam and A. Schilling and M. Shimozono},
  journal={Compositio Mathematica},
  year={2010},
  volume={146},
  pages={811-852}
}
  • Thomas Lam, A. Schilling, M. Shimozono
  • Published 2010
  • Mathematics
  • Compositio Mathematica
  • We construct the Schubert basis of the torus-equivariant K-homology of the ane Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of Peterson in equivariant homology. For the case where G = SLn, the K-homology of the ane Grassmannian is identied with a sub-Hopf algebra of the ring of symmetric functions. The Schubert basis is represented by inhomogeneous symmetric functions, called K-k-Schur… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 60 REFERENCES
    Schubert polynomials for the affine Grassmannian
    • 89
    • Highly Influential
    • PDF
    Kostant polynomials and the cohomology ring for G/B.
    • 126
    • PDF
    Notes on Schubert classes of a loop group
    • 9
    • Highly Influential
    • PDF