Affine Insertion And Pieri Rules For The Affine Grassmannian
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Affine Insertion and Pieri Rules for the Affine Grassmannian
Author | : Thomas Lam |
Publisher | : American Mathematical Soc. |
Total Pages | : 103 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821846582 |
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The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, 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 $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.
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