Memoirs of the American Mathematical Society 2010; 82 pp; softcover Volume: 208 ISBN-10: 0-8218-4658-2 ISBN-13: 978-0-8218-4658-2 List Price: US$67 Individual Members: US$40.20 Institutional Members: US$53.60 Order Code: MEMO/208/977
![[Add Item]](/images/addtocart.gif) | 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.
 Table of Contents
- Schubert bases of \(\mathrm{Gr}\) and symmetric functions
- Strong tableaux
- Weak tableaux
- Affine insertion and affine Pieri
- The local rule \(\phi_{u,v}\)
- Reverse local rule
- Bijectivity
- Grassmannian elements, cores, and bounded partitions
- Strong and weak tableaux using cores
- Affine insertion in terms of cores
- Bibliography
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