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Affine Insertion and Pieri Rules for the Affine Grassmannian
| eBook ISBN: | 978-1-4704-0591-5 |
| Product Code: | MEMO/208/977.E |
| List Price: | $71.00 |
| MAA Member Price: | $63.90 |
| AMS Member Price: | $42.60 |
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Affine Insertion and Pieri Rules for the Affine Grassmannian
| eBook ISBN: | 978-1-4704-0591-5 |
| Product Code: | MEMO/208/977.E |
| List Price: | $71.00 |
| MAA Member Price: | $63.90 |
| AMS Member Price: | $42.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 208; 2010; 82 ppMSC: Primary 05; 14
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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Table of Contents
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Chapters
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Introduction
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1. Schubert Bases of $\mathrm {Gr}$ and Symmetric Functions
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2. Strong Tableaux
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3. Weak Tableaux
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4. Affine Insertion and Affine Pieri
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5. The Local Rule $\phi _{u,v}$
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6. Reverse Local Rule
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7. Bijectivity
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8. Grassmannian Elements, Cores, and Bounded Partitions
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9. Strong and Weak Tableaux Using Cores
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10. Affine Insertion in Terms of Cores
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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Volume: 208; 2010; 82 pp
MSC: Primary 05; 14
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.
-
Chapters
-
Introduction
-
1. Schubert Bases of $\mathrm {Gr}$ and Symmetric Functions
-
2. Strong Tableaux
-
3. Weak Tableaux
-
4. Affine Insertion and Affine Pieri
-
5. The Local Rule $\phi _{u,v}$
-
6. Reverse Local Rule
-
7. Bijectivity
-
8. Grassmannian Elements, Cores, and Bounded Partitions
-
9. Strong and Weak Tableaux Using Cores
-
10. Affine Insertion in Terms of Cores
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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