LEADER 04003nam 2200577 450 001 9910812402203321 005 20170816143334.0 010 $a1-4704-0591-1 035 $a(CKB)3360000000465161 035 $a(EBL)3114261 035 $a(SSID)ssj0000888761 035 $a(PQKBManifestationID)11533775 035 $a(PQKBTitleCode)TC0000888761 035 $a(PQKBWorkID)10866472 035 $a(PQKB)10775321 035 $a(MiAaPQ)EBC3114261 035 $a(RPAM)16372704 035 $a(PPN)195418670 035 $a(EXLCZ)993360000000465161 100 $a20150416h20102010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAffine insertion and Pieri rules for the affine Grassmannian /$fThoman Lam, [and others] 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2010. 210 4$dİ2010 215 $a1 online resource (82 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 977 300 $a"Volume 208, number 977 (second of 6 numbers)." 311 $a0-8218-4658-2 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""Chapter 9. Strong and Weak Tableaux Using Cores""""9.1. Weak tableaux on cores are k-tableaux""; ""9.2. Strong tableaux on cores""; ""9.3. Monomial expansion of t-dependent k-Schur functions""; ""9.4. Enumeration of standard strong and weak tableaux""; ""Chapter 10. Affine Insertion in Terms of Cores""; ""10.1. Internal insertion for cores""; ""10.2. External insertion for cores (Case X)""; ""10.3. An example""; ""10.4. Standard case""; ""10.5. Coincidence with RSK as n""; ""10.6. The bijection for n = 3 and m = 4""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 977. 606 $aGeometry, Affine 606 $aCombinatorial analysis 615 0$aGeometry, Affine. 615 0$aCombinatorial analysis. 676 $a516/.4 702 $aLam$b Thomas$f1980- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812402203321 996 $aAffine insertion and Pieri rules for the affine Grassmannian$94082101 997 $aUNINA