Index
P –frame bundle, 274, 384, 421, 605
normal, 277
W
p
, 325
Wp , 325
Σ–height, 292
α–string through β, 167
r–determined, 562
|1|–grading, 296
|k|–grading, 238
absolute derivative, 38
action, 24
effective, 25
free, 25
transitive, 25
adjoint action, 20
admissible
family of curves, 110
affine extension, 47
AHS structure, 137
algebraic bracket
of adjoint tractors, 85
ambient connection
for contact projective structures, 582
for projective structures, 528
ambient metric, 531
associated bundle, 28
associated graded
vector space, 235
atlas, 15
automorphism, 163
infinitesimal, 97
inner, 163
Bianchi identity
general, 88
reductive, 90
biholomorphism, 32
Borel fixed point theorem, 307
Borel subalgebra, 291
standard, 184, 291
Borel–Moore homology, 337
Borel–Weil theorem, 185
Bott–Borel–Weil theorem, 357
Kostant’s version, 351
Bruhat decomposition, 333
Bruhat order, 324
bundle of scales, 503
conformal, 124
canonical curves
in Cartan geometries, 110
on homogeneous spaces, 69
preferred parametrization, 568
Carnot group, 267
Cartan connection, 71
conformal, 128
Cartan decomposition, 202
global, 206
Cartan geometry, 71
Cartan involution, 202
global, 206
Cartan matrix, 169
Cartan product, 186
Cartan subalgebra
θ–stable, 213
complex, 162
maximally compact, 213
maximally noncompact, 213
real, 200, 213
Cartan’s criteria, 150
Casimir element, 190
Casimir operator
of a representation, 152
center
of a Lie algebra, 144
of the universal enveloping algebra, 192
central character, 192
centralizer, 163
chains, 574, 584, 591
character, 194
chart, 15
Christoffel symbols, 39
cocycle
of transition functions, 27
commutator ideal, 142
complete reducibility, 152
complexification
623
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