04748nam 2200601 450 991048059520332120170822144313.00-8218-9874-4(CKB)3780000000000141(EBL)3114577(SSID)ssj0000889146(PQKBManifestationID)11502924(PQKBTitleCode)TC0000889146(PQKBWorkID)10876266(PQKB)10667643(MiAaPQ)EBC3114577(PPN)195408349(EXLCZ)99378000000000014120150416h20122012 uy 0engur|n|---|||||txtccrThe poset of k-shapes and branching rules for k-Schur functions /Thomas Lam [and three others]Providence, Rhode Island :American Mathematical Society,2012.©20121 online resource (101 p.)Memoirs of the American Mathematical Society,1947-6221 ;Volume 223, Number 1050"May 2013 , Volume 223, Number 1050 (fourth of 5 numbers)."0-8218-7294-X Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 223, Number 1050.Partially ordered setsSchur functionsElectronic books.Partially ordered sets.Schur functions.516.3/5Lam Thomas1980-MiAaPQMiAaPQMiAaPQBOOK9910480595203321The poset of k-shapes and branching rules for k-Schur functions2211392UNINA