Index
action, 24
acyclic, 49
additive group (G
a
), 20, 22, 58, 101, 105
adjoint group, 158
adjoint representation, 108, 130, 286
affine scheme, 5, 14
affine space (A), 5, 98
affine variety, 4, 9, 125
affine Weyl group, 231-240
alcove, 232-240
algebraic group, 19
algebraic scheme, 9, 16
ample 203, 270, 375
antipode, 21, 112
associated bundle, 80, 202
associated faisceau, 68
associated fibration, 78-81
associated graded group, 132
associated sheaf, 74-77, 79-83
on flag varieties and Schubert schemes
201-205, 366-368, 371-374, 376-383
augmentation, 21
augmentation ideal, 22
automorphism, 19
base change
and cohomology, 29, 54, 57
for distributions, 98
for functors, 13, 68, 70
and homomorphisms, 142-143
and induction, 40, 54, 57
and injective hulls, 144-145
for modules, 26, 148
for quotients, 71
for Schubert schemes, 377
for Schur algebras, 403
for simple modules, 180, 194
for tilting modules, 458, 474
for Weyl modules, 272
base map, 50, 90, 323
big cell, 160
block, 252, 311, 317
Borel-Bott-Weil theorem, 221, 307
Borel subgroup, 159
Bott-Samelson scheme, 360
Bruhat cell, 353, 356, 361
Bruhat decomposition, 160, 355
Bruhat order, 360
canonical sheaf, 202, 483
canonical splitting, 502-503
central character, 246
centraliser, 24, 32, 105, 107, 109
central subgroup, 20
centre, 25, 158
character group, 22
close, 247
closed set of roots, 159, 353
closed subfunctor, 7, 9, 14-16, 83
closed subgroup, 20
closure, 7, 15, 83, 232, 261
coadjoint representation, 214
coalgebra, 99
cocommutative, 21, 113
coefficient space, 394
cohomology groups, 50-54
for additive groups, 58-64
for finite group schemes, 133-139
for Probenius kernels, 343-345, 348, 350
and Hochschild complex, 55-58
for reductive groups and parabolic
subgroups, 206, 208-209, 230, 411-413
coinduced module, 119-123, 191-193,
292-293
coinverse, 21
commutative group, 20
comodule, 27, 114
comorphism, 6
compatibly split, 489
composition factor, 34
composition series, 34
comultiplication, 21, 112
conjugation map, 23
conjugation representation, 26, 27, 214
constant term, 96
contravariant form, 281, 283, 401
coroot, 156
cotangent bundle, 245
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