Index
abelian extension, maximal, 249
absolute trace formula, 444
abstract Cartan matrix, 6
abstract Fourier transform, 195
abstract harmonic analysis, 195
abstract root system, 4
acceptable, 93
additive, 333
adele, 254
adjoint lifting, 342
adjoint representation, 298
admissible (g, K)-module, 68, 138
admissible homomorphism, 258, 277, 278,
294
admissible module, 276
admissible representation, 68, 75, 134, 311
algebraic group
linear, 267
ramified at a place, 414
split at a place, 382, 414
unramified at a place, 382
algebraically integral, 9, 18
almost all, 254
along the walls, 146
analytic vector, 69
analytically integral, 18
anisotropic, 433
approximately unital, 275, 276
archimedean, 246
Arthur's conjecture, 460
Artin Conjecture, 267, 283, 334
Artin L function, 264, 332
Artin map, 260, 261
Artin product formula, 256
Artin reciprocity, 260, 261
Artin symbol, 260
associated 0-stable parabolic, 231
associated vector bundle, 123
Atiyah's L2 Index Theorem, 103
automorphic form, 274, 328, 364, 391, 461
automorphic function, 325
automorphic induction, 343, 421
automorphic L function, 458
automorphic module, 276
automorphic representation, 276, 325, 328,
461
cuspidal, 276, 328
base change, 299, 343, 422, 450
base change lift, 345, 425
belong, 445
Blattner's Conjecture, 105
Borel subalgebra, 26, 83
Borel subgroup, 84
Borel-Harish-Chandra theorem, 384
Borel-Weil Theorem, 85, 115
Borel-Weil-Bott Theorem, 85 121
bounded at 00, 94
Brauer's Induction Theorem, 267
Bruhat decomposition, 25, 136, 305
Bruhat order, 36
bundle
associated vector, 123
canonical, 85
homogeneous vector, 123
C°° vector, 63
canonical bundle, 85
Cartan decomposition, 21, 22, 305
Cartan involution, 20
Cartan matrix, 5
abstract, 6
Cartan subalgebra, 2, 16, 24, 78
Cartan subgroup, 24
Cartan subspace, 194
Cartan's criterion, 1
Casimir element, 11
Casselman-Osborne Lemma, 100
Cayley transform, 24
central character, 335
character, 13, 158, 168
distribution, 77
global, 77, 91
infinitesimal, 73
Chevalley's Lemma, 7
class field theory
global, 261
local, 250
473
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