04003nam 2200577 450 991078885960332120170816143334.01-4704-0591-1(CKB)3360000000465161(EBL)3114261(SSID)ssj0000888761(PQKBManifestationID)11533775(PQKBTitleCode)TC0000888761(PQKBWorkID)10866472(PQKB)10775321(MiAaPQ)EBC3114261(RPAM)16372704(PPN)195418670(EXLCZ)99336000000046516120150416h20102010 uy 0engur|n|---|||||txtccrAffine insertion and Pieri rules for the affine Grassmannian /Thoman Lam, [and others]Providence, Rhode Island :American Mathematical Society,2010.©20101 online resource (82 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 977"Volume 208, number 977 (second of 6 numbers)."0-8218-4658-2 Includes bibliographical references.""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""""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""""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""""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""Memoirs of the American Mathematical Society ;Number 977.Geometry, AffineCombinatorial analysisGeometry, Affine.Combinatorial analysis.516/.4Lam Thomas1980-MiAaPQMiAaPQMiAaPQBOOK9910788859603321Affine insertion and Pieri rules for the affine Grassmannian3864143UNINA