Poset of k-Shapes and Branching Rules for k-Schur Functions.

Intro -- 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 =∅) -- 8.4. Commuting cube (degenerate case =∅) -- 8.5. Commuting cube (degenerate case =∅) -- 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 -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.