The poset of k-shapes and branching rules for k-Schur functions / / Thomas Lam [and three others]

• Record Nr.: UNINA9910796038703321
• Autore: Lam Thomas <1980->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• ISBN: 0-8218-9874-4
• Descrizione fisica: 1 online resource (101 p.)
• Collana: Memoirs of the American Mathematical Society, , 1947-6221 ; ; Volume 223, Number 1050
• Disciplina: 516.3/5
• Soggetti: Partially ordered sets; Schur functions
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "May 2013 , Volume 223, Number 1050 (fourth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• 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""