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Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others]
| Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (82 p.) |
| Disciplina | 516/.4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Affine
Combinatorial analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0591-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 (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"" |
| Record Nr. | UNINA-9910480248803321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others]
| Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (82 p.) |
| Disciplina | 516/.4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Affine
Combinatorial analysis |
| ISBN | 1-4704-0591-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 (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"" |
| Record Nr. | UNINA-9910788859603321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others]
| Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (82 p.) |
| Disciplina | 516/.4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Affine
Combinatorial analysis |
| ISBN | 1-4704-0591-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 (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"" |
| Record Nr. | UNINA-9910812402203321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others]
| The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others] |
| Autore | Lam Thomas <1980-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (101 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Partially ordered sets
Schur functions |
| ISBN | 0-8218-9874-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""1.1. -Schur functions and branching coefficients""; ""1.2. The poset of -shapes""; ""1.3. -shape functions""; ""1.4. Geometric meaning of branching coefficients""; ""1.5. -branching polynomials and strong -tableaux""; ""1.6. Tableaux atoms and bijection (1.20)""; ""1.7. Connection with representation theory""; ""1.8. Outline""; ""Acknowledgments""; ""Chapter 2. The poset of -shapes""; ""2.1. Partitions""; ""2.2. -shapes""; ""2.3. Strings""; ""2.4. Moves""; ""2.5. Poset structure on -shapes""
""2.6. String and move miscellany""""Chapter 3. Equivalence of paths in the poset of -shapes""; ""3.1. Diamond equivalences""; ""3.2. Elementary equivalences""; ""3.3. Mixed elementary equivalence""; ""3.4. Interfering row moves and perfections""; ""3.5. Row elementary equivalence""; ""3.6. Column elementary equivalence""; ""3.7. Diamond equivalences are generated by elementary equivalences""; ""3.8. Proving properties of mixed equivalence""; ""3.9. Proving properties of row equivalence""; ""3.10. Proofs of Lemma 3.18 and Lemma 3.19""; ""Chapter 4. Strips and tableaux for -shapes"" ""4.1. Strips for cores""""4.2. Strips for -shapes""; ""4.3. Maximal strips and tableaux""; ""4.4. Elementary properties of \ _{\ }^{( )}[ ] and \ _{\ }^{( )}[ ]""; ""4.5. Basics on strips""; ""4.6. Augmentation of strips""; ""4.7. Maximal strips for cores""; ""4.8. Equivalence of maximal augmentation paths""; ""4.9. Canonical maximization of a strip""; ""Chapter 5. Pushout of strips and row moves""; ""5.1. Reasonableness""; ""5.2. Contiguity""; ""5.3. Interference of strips and row moves""; ""5.4. Row-type pushout: non-interfering case"" ""5.5. Row-type pushout: interfering case""""5.6. Alternative description of pushouts (row moves)""; ""Chapter 6. Pushout of strips and column moves""; ""6.1. Reasonableness""; ""6.2. Normality""; ""6.3. Contiguity""; ""6.4. Interference of strips and column moves""; ""6.5. Column-type pushout: non-interfering case""; ""6.6. Column-type pushout: interfering case""; ""6.7. Alternative description of pushouts (column moves)""; ""Chapter 7. Pushout sequences""; ""7.1. Canonical pushout sequence""; ""7.2. Pushout sequences from ( , ) are equivalent"" ""Chapter 8. Pushouts of equivalent paths are equivalent""""8.1. Pushout of equivalences""; ""8.2. Commuting cube (non-degenerate case)""; ""8.3. Commuting cube (degenerate case =â??)""; ""8.4. Commuting cube (degenerate case =â??)""; ""8.5. Commuting cube (degenerate case =â??)""; ""Chapter 9. Pullbacks""; ""9.1. Equivalences in the reverse case""; ""9.2. Reverse operations on strips""; ""9.3. Pullback of strips and moves""; ""9.4. Pullbacks sequences are all equivalent""; ""9.5. Pullbacks of equivalent paths are equivalent""; ""9.6. Pullbacks are inverse to pushouts"" ""Appendix A. Tables of branching polynomials"" |
| Record Nr. | UNINA-9910796038703321 |
Lam Thomas <1980->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others]
| The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others] |
| Autore | Lam Thomas <1980-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (101 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Partially ordered sets
Schur functions |
| ISBN | 0-8218-9874-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""1.1. -Schur functions and branching coefficients""; ""1.2. The poset of -shapes""; ""1.3. -shape functions""; ""1.4. Geometric meaning of branching coefficients""; ""1.5. -branching polynomials and strong -tableaux""; ""1.6. Tableaux atoms and bijection (1.20)""; ""1.7. Connection with representation theory""; ""1.8. Outline""; ""Acknowledgments""; ""Chapter 2. The poset of -shapes""; ""2.1. Partitions""; ""2.2. -shapes""; ""2.3. Strings""; ""2.4. Moves""; ""2.5. Poset structure on -shapes""
""2.6. String and move miscellany""""Chapter 3. Equivalence of paths in the poset of -shapes""; ""3.1. Diamond equivalences""; ""3.2. Elementary equivalences""; ""3.3. Mixed elementary equivalence""; ""3.4. Interfering row moves and perfections""; ""3.5. Row elementary equivalence""; ""3.6. Column elementary equivalence""; ""3.7. Diamond equivalences are generated by elementary equivalences""; ""3.8. Proving properties of mixed equivalence""; ""3.9. Proving properties of row equivalence""; ""3.10. Proofs of Lemma 3.18 and Lemma 3.19""; ""Chapter 4. Strips and tableaux for -shapes"" ""4.1. Strips for cores""""4.2. Strips for -shapes""; ""4.3. Maximal strips and tableaux""; ""4.4. Elementary properties of \ _{\ }^{( )}[ ] and \ _{\ }^{( )}[ ]""; ""4.5. Basics on strips""; ""4.6. Augmentation of strips""; ""4.7. Maximal strips for cores""; ""4.8. Equivalence of maximal augmentation paths""; ""4.9. Canonical maximization of a strip""; ""Chapter 5. Pushout of strips and row moves""; ""5.1. Reasonableness""; ""5.2. Contiguity""; ""5.3. Interference of strips and row moves""; ""5.4. Row-type pushout: non-interfering case"" ""5.5. Row-type pushout: interfering case""""5.6. Alternative description of pushouts (row moves)""; ""Chapter 6. Pushout of strips and column moves""; ""6.1. Reasonableness""; ""6.2. Normality""; ""6.3. Contiguity""; ""6.4. Interference of strips and column moves""; ""6.5. Column-type pushout: non-interfering case""; ""6.6. Column-type pushout: interfering case""; ""6.7. Alternative description of pushouts (column moves)""; ""Chapter 7. Pushout sequences""; ""7.1. Canonical pushout sequence""; ""7.2. Pushout sequences from ( , ) are equivalent"" ""Chapter 8. Pushouts of equivalent paths are equivalent""""8.1. Pushout of equivalences""; ""8.2. Commuting cube (non-degenerate case)""; ""8.3. Commuting cube (degenerate case =â??)""; ""8.4. Commuting cube (degenerate case =â??)""; ""8.5. Commuting cube (degenerate case =â??)""; ""Chapter 9. Pullbacks""; ""9.1. Equivalences in the reverse case""; ""9.2. Reverse operations on strips""; ""9.3. Pullback of strips and moves""; ""9.4. Pullbacks sequences are all equivalent""; ""9.5. Pullbacks of equivalent paths are equivalent""; ""9.6. Pullbacks are inverse to pushouts"" ""Appendix A. Tables of branching polynomials"" |
| Record Nr. | UNINA-9910827633703321 |
|
Lam Thomas <1980->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others]
| The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (101 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Partially ordered sets
Schur functions |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-9874-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""1.1. -Schur functions and branching coefficients""; ""1.2. The poset of -shapes""; ""1.3. -shape functions""; ""1.4. Geometric meaning of branching coefficients""; ""1.5. -branching polynomials and strong -tableaux""; ""1.6. Tableaux atoms and bijection (1.20)""; ""1.7. Connection with representation theory""; ""1.8. Outline""; ""Acknowledgments""; ""Chapter 2. The poset of -shapes""; ""2.1. Partitions""; ""2.2. -shapes""; ""2.3. Strings""; ""2.4. Moves""; ""2.5. Poset structure on -shapes""
""2.6. String and move miscellany""""Chapter 3. Equivalence of paths in the poset of -shapes""; ""3.1. Diamond equivalences""; ""3.2. Elementary equivalences""; ""3.3. Mixed elementary equivalence""; ""3.4. Interfering row moves and perfections""; ""3.5. Row elementary equivalence""; ""3.6. Column elementary equivalence""; ""3.7. Diamond equivalences are generated by elementary equivalences""; ""3.8. Proving properties of mixed equivalence""; ""3.9. Proving properties of row equivalence""; ""3.10. Proofs of Lemma 3.18 and Lemma 3.19""; ""Chapter 4. Strips and tableaux for -shapes"" ""4.1. Strips for cores""""4.2. Strips for -shapes""; ""4.3. Maximal strips and tableaux""; ""4.4. Elementary properties of \ _{\ }^{( )}[ ] and \ _{\ }^{( )}[ ]""; ""4.5. Basics on strips""; ""4.6. Augmentation of strips""; ""4.7. Maximal strips for cores""; ""4.8. Equivalence of maximal augmentation paths""; ""4.9. Canonical maximization of a strip""; ""Chapter 5. Pushout of strips and row moves""; ""5.1. Reasonableness""; ""5.2. Contiguity""; ""5.3. Interference of strips and row moves""; ""5.4. Row-type pushout: non-interfering case"" ""5.5. Row-type pushout: interfering case""""5.6. Alternative description of pushouts (row moves)""; ""Chapter 6. Pushout of strips and column moves""; ""6.1. Reasonableness""; ""6.2. Normality""; ""6.3. Contiguity""; ""6.4. Interference of strips and column moves""; ""6.5. Column-type pushout: non-interfering case""; ""6.6. Column-type pushout: interfering case""; ""6.7. Alternative description of pushouts (column moves)""; ""Chapter 7. Pushout sequences""; ""7.1. Canonical pushout sequence""; ""7.2. Pushout sequences from ( , ) are equivalent"" ""Chapter 8. Pushouts of equivalent paths are equivalent""""8.1. Pushout of equivalences""; ""8.2. Commuting cube (non-degenerate case)""; ""8.3. Commuting cube (degenerate case =â??)""; ""8.4. Commuting cube (degenerate case =â??)""; ""8.5. Commuting cube (degenerate case =â??)""; ""Chapter 9. Pullbacks""; ""9.1. Equivalences in the reverse case""; ""9.2. Reverse operations on strips""; ""9.3. Pullback of strips and moves""; ""9.4. Pullbacks sequences are all equivalent""; ""9.5. Pullbacks of equivalent paths are equivalent""; ""9.6. Pullbacks are inverse to pushouts"" ""Appendix A. Tables of branching polynomials"" |
| Record Nr. | UNINA-9910480595203321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||