Index
adjoint group, 2, 27
adjoint representation, 2
adjunction morphism, 149, 236
affine Lie algebra, 257
affine reflection, 53
affine Weyl group, 53
alternating function, 39
annihilator of a module, 215
antidominant weight, 54
artinian category, 28
BGG algebra, 260
BGG category, 13
BGG Reciprocity, 65
BGG resolution, 108
block, 30
Borel subalgebra, 2
braid relations, 236
Bruhat cell, 160
Bruhat decomposition, 160
Bruhat ordering, 5
Cartan decomposition, 2
Cartan invariant, 3
Cartan matrix, 257
Cartan subalgebra, 1
category (9, 13
center of U(g), 6
central character, 23
chamber, 133
Chevalley Restriction Theorem, 27
Chevalley-Bruhat ordering, 5
coinvariant algebra, 265, 266
compatible weights, 130
complete module, 246
completion, 246
composition series, 29
contravariant form, 68
convolution, 33
coroot, 3
Coxeter group, 4
direct sum of functors, 214
discrete series, 247
dominant chamber, 133
dominant integral weight, 7
dominant weight, 54
dot action, 24
dot-regular weight, 24
dual root system, 3
duality in 0 , 50
facet, 132
family of twisted Verma modules, 239
filtration, 17
filtration length, 58
flag variety, 122, 160
formal character, 32
fundamental weight, 7
fusion rules, 231
Gabber-Joseph Conjecture, 170
Gelfand-Kirillov dimension, 254
generalized Cartan matrix, 257
generalized KL Conjecture, 172
generalized Verma module, 188
global dimension, 120
Goldie rank, 254
Goldie rank polynomial, 254
Grothendieck group, 29
Harish-Chandra homomorphism, 23
287
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