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Record Nr. |
UNINA9910480248803321 |
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Titolo |
Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others] |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2010 |
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©2010 |
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ISBN |
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Descrizione fisica |
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1 online resource (82 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 977 |
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Disciplina |
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Soggetti |
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Geometry, Affine |
Combinatorial analysis |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Volume 208, number 977 (second of 6 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Contents""; ""Introduction""; ""Chapter 1. Schubert Bases of Gr and Symmetric Functions""; ""1.1. Symmetric functions""; ""1.2. Schubert bases of Gr""; ""1.3. Schubert basis of the affine flag variety""; ""Chapter 2. Strong Tableaux""; ""2.1. n as a Coxeter group""; ""2.2. Fixing a maximal parabolic subgroup""; ""2.3. Strong order and strong tableaux""; ""2.4. Strong Schur functions""; ""Chapter 3. Weak Tableaux""; ""3.1. Cyclically decreasing permutations and weak tableaux""; ""3.2. Weak Schur functions""; ""3.3. Properties of weak strips"" |
""3.4. Commutation of weak strips and strong covers""""Chapter 4. Affine Insertion and Affine Pieri""; ""4.1. The local rule u,v""; ""4.2. The affine insertion bijection u,v""; ""4.3. Pieri rules for the affine Grassmannian""; ""4.4. Conjectured Pieri rule for the affine flag variety""; ""4.5. Geometric interpretation of strong Schur functions""; ""Chapter 5. The Local Rule u,v""; ""5.1. Internal insertion at a marked strong cover""; ""5.2. Definition of u,v""; ""5.3. Proofs for the local rule""; ""Chapter 6. Reverse Local Rule""; ""6.1. Reverse insertion at a cover"" |
""6.2. The reverse local rule""""6.3. Proofs for the reverse insertion""; ""Chapter 7. Bijectivity""; ""7.1. External insertion""; ""7.2. Case A |
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(commuting case)""; ""7.3. Case B (bumping case)""; ""7.4. Case C (replacement bump)""; ""Chapter 8. Grassmannian Elements, Cores, and Bounded Partitions""; ""8.1. Translation elements""; ""8.2. The action of n on partitions""; ""8.3. Cores and the coroot lattice""; ""8.4. Grassmannian elements and the coroot lattice""; ""8.5. Bijection from cores to bounded partitions""; ""8.6. k-conjugate""; ""8.7. From Grassmannian elements to bounded partitions"" |
""Chapter 9. Strong and Weak Tableaux Using Cores""""9.1. Weak tableaux on cores are k-tableaux""; ""9.2. Strong tableaux on cores""; ""9.3. Monomial expansion of t-dependent k-Schur functions""; ""9.4. Enumeration of standard strong and weak tableaux""; ""Chapter 10. Affine Insertion in Terms of Cores""; ""10.1. Internal insertion for cores""; ""10.2. External insertion for cores (Case X)""; ""10.3. An example""; ""10.4. Standard case""; ""10.5. Coincidence with RSK as n""; ""10.6. The bijection for n = 3 and m = 4""; ""Bibliography"" |
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