The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra / / Michael Kapovich, Bernhard Leeb, John J. Millson

• Autore: Kapovich Michael <1963->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2008]; ©2008
• Descrizione fisica: 1 online resource (98 p.)
• Disciplina: 510 s; 512/.482
• Soggetto topico: Semisimple Lie groups; Linear algebraic groups; Geometric group theory; Lorentz groups; Symmetric spaces; Rings (Algebra)
• Persona (resp. second.): LeebBernhard; MillsonJohn J <1946-> (John James)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (pages 82-83).
• Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Roots and Coxeter Groups""; ""2.1. Split tori over F""; ""2.2. Roots, coroots and the Langlands' dual""; ""2.3. Coxeter groups""; ""Chapter 3. The First Three Algebra Problems and the Parameter Spaces â?? for K\G/K""; ""3.1. The generalized eigenvalues of a sum problem Q1 and the parameter space â?? of k-double cosets""; ""3.2. The generalized singular values of a product and the parameter space â?? of K-double cosets""; ""3.3. The generalized invariant factor problem and the parameter space â?? of K-double cosets"" ; ""3.4. Comparison of the parameter spaces for the four algebra problems""""3.5. Linear algebra problems""; ""Chapter 4. The existence of polygonal linkages and solutions to the algebra problems""; ""4.1. Setting up the general geometry problem""; ""4.2. Geometries modeled on Coxeter complexes""; ""4.3. Bruhat-Tits buildings associated with nonarchimedean reductive Lie groups""; ""4.4. Geodesic polygons""; ""Chapter 5. Weighted Configurations, Stability and the Relation to Polygons""; ""5.1. Gauss maps and associated dynamical systems""; ""5.2. The polyhedron D[sub(n)](X)"" ; ""5.3. The polyhedron for the root system B[sub(2)]""""Chapter 6. Polygons in Euclidean Buildings and the Generalized Invariant Factor Problem""; ""6.1. Folding polygons into apartments""; ""6.2. A Solution of Problem Q2 is not necessarily a solution of Problem Q3""; ""Chapter 7. The Existence of Fixed Vertices in Buildings and Computation of the Saturation Factors for Reductive Groups""; ""7.1. The saturation factors associated to a root system""; ""7.2. The existence of fixed vertices""; ""7.3. Saturation factors for reductive groups""; ""Chapter 8. The Comparison of Problems Q3 and Q4"" ; ""8.1. The Hecke ring""""8.2. A geometric interpretation of m[sub(α,β,γ)](0)""; ""8.3. The Satake transform""; ""8.4. A solution of Problem Q4 is a solution of Problem Q3""; ""8.5. A Solution of Problem Q3 is not necessarily a solution of Problem Q4""; ""8.6. The saturation theorem for GL(l)""; ""8.7. Computations for the root systems B[sub(2)] and G[sub(2)] ""; ""Appendix A. Decomposition of Tensor Products and Mumford Quotients of Products of Coadjoint orbits""; ""A. l. The existence of semistable triples and nonzero invariant vectorsin triple tensor products"" ; ""A. 2. The semigroups of solutions to Problems Q1 and Q4""""Bibliography""
• Titolo autorizzato: The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra
• ISBN: 1-4704-0502-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788851503321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; no. 896.