LEADER 04698nam 2200721 450 001 9910827763403321 005 20170822144130.0 010 $a1-4704-0502-4 035 $a(CKB)3360000000465080 035 $a(EBL)3114148 035 $a(SSID)ssj0000888960 035 $a(PQKBManifestationID)11479152 035 $a(PQKBTitleCode)TC0000888960 035 $a(PQKBWorkID)10875130 035 $a(PQKB)10045329 035 $a(MiAaPQ)EBC3114148 035 $a(RPAM)15072359 035 $a(PPN)195417852 035 $a(EXLCZ)993360000000465080 100 $a20071106h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe generalized triangle inequalities in symmetric spaces and buildings with applications to algebra /$fMichael Kapovich, Bernhard Leeb, John J. Millson 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$d©2008 215 $a1 online resource (98 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 896 300 $aDescription based upon print version of record. 311 $a0-8218-4054-1 320 $aIncludes bibliographical references (pages 82-83). 327 $a""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 a??? for K\G/K""; ""3.1. The generalized eigenvalues of a sum problem Q1 and the parameter space a??? of k-double cosets""; ""3.2. The generalized singular values of a product and the parameter space a??? of K-double cosets""; ""3.3. The generalized invariant factor problem and the parameter space a??? of K-double cosets"" 327 $a""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)"" 327 $a""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"" 327 $a""8.1. The Hecke ring""""8.2. A geometric interpretation of m[sub(I?±,I?²,I?³)](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"" 327 $a""A. 2. The semigroups of solutions to Problems Q1 and Q4""""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 896. 606 $aSemisimple Lie groups 606 $aLinear algebraic groups 606 $aGeometric group theory 606 $aLorentz groups 606 $aSymmetric spaces 606 $aRings (Algebra) 615 0$aSemisimple Lie groups. 615 0$aLinear algebraic groups. 615 0$aGeometric group theory. 615 0$aLorentz groups. 615 0$aSymmetric spaces. 615 0$aRings (Algebra) 676 $a510 s 676 $a512/.482 700 $aKapovich$b Michael$f1963-$065692 702 $aLeeb$b Bernhard 702 $aMillson$b John J$g(John James),$f1946- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827763403321 996 $aThe generalized triangle inequalities in symmetric spaces and buildings with applications to algebra$94112177 997 $aUNINA