LEADER 04748nam 2200601 450 001 9910480595203321 005 20170822144313.0 010 $a0-8218-9874-4 035 $a(CKB)3780000000000141 035 $a(EBL)3114577 035 $a(SSID)ssj0000889146 035 $a(PQKBManifestationID)11502924 035 $a(PQKBTitleCode)TC0000889146 035 $a(PQKBWorkID)10876266 035 $a(PQKB)10667643 035 $a(MiAaPQ)EBC3114577 035 $a(PPN)195408349 035 $a(EXLCZ)993780000000000141 100 $a20150416h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 04$aThe poset of k-shapes and branching rules for k-Schur functions /$fThomas Lam [and three others] 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2012. 210 4$dİ2012 215 $a1 online resource (101 p.) 225 1 $aMemoirs of the American Mathematical Society,$x1947-6221 ;$vVolume 223, Number 1050 300 $a"May 2013 , Volume 223, Number 1050 (fourth of 5 numbers)." 311 $a0-8218-7294-X 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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 =a???)""; ""8.4. Commuting cube (degenerate case =a???)""; ""8.5. Commuting cube (degenerate case =a???)""; ""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"" 327 $a""Appendix A. Tables of branching polynomials"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 223, Number 1050. 606 $aPartially ordered sets 606 $aSchur functions 608 $aElectronic books. 615 0$aPartially ordered sets. 615 0$aSchur functions. 676 $a516.3/5 702 $aLam$b Thomas$f1980- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480595203321 996 $aThe poset of k-shapes and branching rules for k-Schur functions$92211392 997 $aUNINA