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| Garrett P. — Buildings and Classical Groups |
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| Предметный указатель |
Adjacent 3.1
Adjacent, s- 3.1
Affine, building 14.1
Affine, combination 12.1
Affine, Coxeter complex 13.4 13.6
Affine, Coxeter system 2.2 13.4
Affine, functional 12.1
Affine, Hecke algebra 6.1 6.2
Affine, hyperplane 12.1
Affine, independence 12.1
Affine, reflection group 13.3
Affine, span 12.1
Affine, Weyl group 12.5 13.3 17.2
Alcove 12.5
Alternating form 7.2
Alternating space 7.2
Anisotropic space 7.2
Antipodal chamber 4.6
Apartment 4.1
Apartment system 4.1
BN-pair 5.1
BN-pair, spherical 5.6
Borel subgroup 5.6
Bornological group 14.6
Bornology 14.6
Bounded set 14.6
Bruhat — Tits decomposition 5.3 5.4
Bruhat, decomposition 5.1 5.4 17.4
Bruhat, order on Coxeter groups 1.8
Building at infinity 16.9
Building, affine 14.1
Building, definition 4.1
Building, metric 14.2
Building, spherical 4.6
Canonical metric on affine building 14.2
Canonical metric on affine complex 13.7
Canonical retraction 4.2
Cartan decomposition 17.5
Cdimension f face 3.1
Cell multiplication rules 5.1
Chamber 3.1
Chamber complex 3.1
Cmbinatorial convexity of apartments 4.5
Cmbinatorial convexity of half-apartments 3.6
Compact subgroups 4.1.4
Compact subgroups, conjugacy 14.7
Compact subgroups, good 14.8
Complete, apartment system 4.4
Complete, discrete valuation ring 4.1.2
Complex, chamber 3.1
Complex, Coxeter 3.4
Complex, simplicial 3.1
Configurations of chamber and sector 16.5
Configurations of sector and three chambers 16.6
Configurations of three chambers 15.4
Configurations of two sectors 16.7
Conical cell 16.9
Conjugacy classes of maximal compacts 14.7
Conjugacy classes of parabolics 5.6
Connected Coxeter diagram 1.2
Convexity of apartments 4.5
Convexity of half-apartments 3.6
Convolution product 6.2
Coroot 12.5
Cosine inequality 17.4
Coxeter, complex 3.4
Coxeter, data 1.2
Coxeter, diagram 1.2
Coxeter, form 1.3
Coxeter, group 1.2
Coxeter, poset 3.4
Coxeter, system 1.2
Crcumcenter 14.6
Crcumradius 14.6
Cross, a wall 3.3
Crystallographic, root system 12.5
Crystallographic, Weyl group 12.5
Deletion condition 1.7
Diameter of building 4.6
Diameter of chamber 13.7
Diameter of chamber complex 4.6
Dihedral group 1.2
Dimension of simplex 3.1
Dimension of simplicial complex 3.1
Discrete, valuation 4.1.2
Discrete, valuation ring 4.1.2
Ends of tree 16.9
Essential, reflection group 12.3
Face at infinity 16.9
Face of simplex 3.1
Face, relation 3.1
Facet 3.1
Finite Coxeter group 1.5
Finite reflection group 12.3
Fixed-point theorem 14.6
Flag of totally isotropic subspaces 10.1
Flag, complex 3.1
Folding 3.3
Folding, reversible 3.3
gallery 3.1
Gallery, non-stuttering 3.1
Gallery, stuttering 3.1
Generic algebra 6.1
Geodesic ray 16.8
Geodesics 13.7 14.2
Geometric realization of simplicial complex 13.5
Geometric realization of simplicial map 13.5
Good, maximal bounded subgroup 14.8
Good, maximal compact subgroup 14.8
Good, vertex 12.4 14.8
Greatest lower bound in poset 3.1
Group, algebra 6.1 6.3
Group, dihedral 1.2
Group, general linear 7.1
Group, orthogonal 7.2
Group, special linear 7.1
Group, special orthogonal 7.2
Group, symplectic 7.2
Group, unitary 7.2
Half-apartment 3.3
Half-space 3.3
Hecke algebra 6.2
Hermitian form 7.1
Hermitian space 7.1
Homothety 4.2.1
Homothety class 4.2.1
Hyperbolic pair 7.2
Hyperbolic plane 7.2
Hyperbolic space 7.2
Hyperplane 12.1
Ideal point 16.9
| Incidence geometry 3.1
Indecomposable 1.2 12.4 13.1 13.4
Infimum in poset 3.1
Involution 7.2
Isometry, group 7.2
Isometry, strong 15.5
Isotropic, subspace 7.2
Isotropic, vector 7.2
Iwahori — Hecke algebra 6.2
Iwahori, decomposition 17.7
Iwahori, subgroup 14.1 17.2
Iwasawa decomposition 17.6
Kernel of formed space 7.2
Label of canonical of Coxeter complex 3.4
Label of simplex 3.1
Label of simplicial complex 3.1
Lattice 4.1.4
Length of word 1.1
Levi component 5.6 7.4 17.2
Linear part of affine map 12.4 14.8 16.9
Linear reflection group 12.3
Link 4.4
Local finiteness hyperplanes 12.1
Local finiteness of building 6.2
Local finiteness Tits’ cones 13.4
Map of simplicial complexes 3.1
Maximal apartment system 4.4
Maximal bounded subgroup 14.7
Maximal compact subgroup 14.7
Maximal length element in finite Coxeter group 1.5
Metric on affine building 14.2
Metric on affine complex 13.7
Minimal gallery 3.1
Minimal parabolic subgroup 5.6 7.4 17.2
Monomial matrix 9.3 10.3
Mutually incident 3.1
Negative curvature inequality 14.3
Non-degenerate formed space 7.2
Opposite chamber 4.6
Opposite folding 3.3
Opposite parabolic 5.6
Opposite side of wall 3.3
Oriflamme, double affine complex 2.2 4.5.1
Oriflamme, single affine complex 2.2 4.6.1
Oriflamme, spherical complex 2.1 11.1
p-adic, integers 4.1.1
p-adic, metric 4.1.1
p-adic, numbers 4.1.1
Panel in wall 3.3
Parabolic subgroup 1.9 5.6 7.4 17.2
Parahoric subgroup 17.2 17.3
Perron — Frobenius lemma 13.3
POSET 3.1
Positive half-apartment with respect to sector 16.6
Presentation of group 1.1
Product, convolution 6.2
Product, twisted tensor 6.3
Quadratic, form 7.2
Quadratic, space 7.2
Reduced, gallery 15.1
Reduced, root system 12.3
Reduced, word 1.1
Reflection 1.3 3.3 12.1
Reflection, associated to folding 3.3
Retraction 3.1
Retraction to apartment, attached to sector 16.5
Retraction to apartment, centered at chamber 4.2
Reversible folding 3.3
Root 1.4 12.3
Root system 12.3
Root system, affine 12.5
Root system, crystallographic 12.5
Root system, spherical 12.3
Root, negative 1.4
Root, positive 1.4
Root, simple 12.3
s-adjacent 3.1 3.6
Sector in apartment 16.1
Sector in building 16.5
Separated by a wall 3.3
Similitude 13.7 14.2
Similitude group 7.2
Simple root 12.3
simplex 3.1
Simplex-like poset 3.1
Simplicial complex 3.1
Simplicial cone 12.3
Special subgroup of BN-pair 5.1 5.5
Special subgroup of Coxeter group 1.9
Special subgroup of group with BN-pair 5.3
Special vertex 12.4 14.8 14.9
Spherical buildings 4.6
Spherical Coxeter complex 4.6 13.2
Spherical reflection group 12.3
Spherical Weyl group 1.5 5.6 12.5 17.2
Strong exchange condition 1.7
Strong transitivity 5.2
Structure constants 6.1
Subcomplex 3.1
Subexpression 1.9
Symplectic group 7.2
System, Coxeter 1.2
Thick building 4.1
Thick chamber complex 3.1
Thin chamber complex 3.1
Tits system 5.1
Tits’ cones 13.1
Topological group 17.7
Totally isotropic subspace 7.2
TREE 14.1
Twisted multiplication 6.3
Twisted tensor product 6.3
Type of flag in vectorspace 7.1 9.2
Type of flag, of isotropic subspaces 10.2
Type of gallery 3.5 15.1
Type of parabolic in GL(n) 7.1
Type of simplex 3.1
Type,  ,  ,  2.1
Type,  ,  ,  ,  2.2
Typing of simplicial complex 3.1
Unipotent radical 7.4
Uniqueness lemma 3.2
Unitary group 7.2
Vertex in incidence geometry 3.1
Vertex in simplicial complex 3.1
wall 3.3 12.1
Wall, crossed by gallery 3.3
Weyl group, affine 12.5 14.8 17.2
Weyl group, crystallographic 12.5
Weyl group, spherical 1.5 12.5 14.8 17.2
Witt theorem 7.3
Word 1.1
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