Index of terminology
action (of algebraic group on variety), 637
adjoint action, 637
admissible ideal, 142
admissible ordering, 450
affme algebraic group, 633
reductive ~, 636
semisimple ~, 636
algebra, 7, 230
associative law in an ~, 231
basic ~, 167
cellular ~, 720
coordinate ~, 14
graded ~, 11
Green ~, 524
Hecke ~, 203
hereditary ~, 169, 177
Lusztig ~, 527
quasi-hereditary ~, 704
tensor ~ , 10, 142
unit law in an ~, 231
v-exterior ~, 14
^-symmetric ~, 13
almost split sequence, 83, 107
asymptotic algebra, 360, 393
Auslander-Buchsbaum equality, 710
Auslander-Reiten sequence, 107
Auslander-Reiten translation, 112
basis verification trick, 15, 241, 259
BGP reflection functor, 60
bialgebra, 235
~ homomorphism, 236
biideal i n a ~ , 236
opposite ~, 237
big cell, 641
BLM algebra, 596
BLM basis, 587, 606
~ o f 5 ( n , r ) , 587
- of U, 606
Borel fixed point theorem, 638
Borel subgroup, 212, 639
braid group, 193
Brauer theory, 729
Bruhat decomposition, 214, 641
canonical basis, 22
~ for a Hecke algebra, 328
~ for a quantum Schur algebra, 416
~ for a quantum enveloping algebra, 497
~ of a standard module, 423
Cartan datum, 35, 523
Cartan matrix, 2
~ of affine type, 2
~ of finite type, 2
~ of wild type, 2
graph realization of ~, 4
indecomposable ~, 4
root datum realization of ~, 4
symmetrizable ~, 2
symmetrization of ~, 2
Casimir element, 296
- of IMsfo), 296
cell, 325
~ module, 349, 721
~ representation, 721
filtration, 350
left ~, 335
right ~, 335
two-sided ~, 335
cellular basis, 720
cellular datum, 720
cellular property, 389, 421
755
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