Affine insertion and Pieri rules for the affine Grassmannian / / Thoman Lam, [and others]

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2010; ©2010
• Descrizione fisica: 1 online resource (82 p.)
• Disciplina: 516/.4
• Soggetto topico: Geometry, Affine; Combinatorial analysis
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): LamThomas <1980->
• Note generali: "Volume 208, number 977 (second of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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""
• Titolo autorizzato: Affine insertion and Pieri rules for the affine Grassmannian
• ISBN: 1-4704-0591-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480248803321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Number 977.