C O ] 2 3 N ov 2 00 8 Affine insertion and Pieri rules for the affine Grassmannian

  title={C O ] 2 3 N ov 2 00 8 Affine insertion and Pieri rules for the affine Grassmannian},
  author={Thomas Lam and Luc Lapointe and Jennifer Morse and Mark Shimozono},
We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n, C). Our main results are: • Pieri rules for the Schubert bases of H∗(Gr) and H∗(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. • A new combinatorial definition for k-Schur functions, which represent the Schubert basis of H∗(Gr). • A combinatorial interpretation of the pairing H∗(Gr)×H∗(Gr) → Z. These results are… CONTINUE READING
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