Index
Abramenko, 64
adjacent, 6, 36
adjoint representation, x, 20
AdK-
diagonalizable, 20
locally finite, 20
locally unipotent, 20
semisimple, 20
affine, 64
Coxeter group, 63
anisotropic kernel, 38
apartment, 6
basis
standard, 5
Borel, ix, xii, 23
Borel subgroup, 9
bounded subgroup, xi, 17
bounded unipotent, 18
boundedly generated, 12
Bridson, xii, 13, 45
Bruhat-Tits tree, 14
building, 6
thick, 6
twin, 6
Cartan matrix
2-spherical, 2
classical, 1
generalized, ix, 1
symmetrizable, 1
CAT(0)
inequality, 11
polyhedral complex, 13
space, 11
Chevalley involution, 73
Chosson, 53
codistance, 6
combinatorial convex closure, 36
combinatorially convex, 14, 36
compact form, 73
compact involution, 73
completely reducible, 35
coregular subgroup, 39
regular subgroup, 38
coregular, 33, 39
coroot lattice, 66, 67
diagonal automorphism, 23, 28
diagonal-by-sign, x
diagonalizable algebraic group, 70
diagonalizable subgroup, 9
coregular, 33
regular, 31
diagram automorphism
exceptional, 53
standard, 53
distance function, 6
geodesic
line, 11
metric space, 11
path, 11
segment, 11
triangle, 11
geometric representation, 64
H-chambers, 36
ee, 53
half-apartments, 7
half-space, 37
isometry
elliptic, 11
hyperbolic, 11, 13
semisimple, 11
Kac, ix, xiii, 21, 22, 74, 75
Kac-Moody
algebra, 1, 19
group, 2
root datum, 1
Levi factor, 18
Levi subgroup, 18
locally finite field, 54
uhlherr, xii, 35, 36
Moody, ix
Moufang, 8
83
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