Index
abelian category, 116, 117
abelian subcategory, 118
abelian variety, 421
acyclic
objects for a functor, 130
sheaves, 159
additive category, 116
additive functor, 116
adjacent Weyl chambers, 479
adjoint of an operator, 360
adjoint representation, 384
adjunction morphisms, 155
admissible representation, 485
afRne variety, 186
algebraic
element, 62
field extension, 62
group, 376, 419
group action, 424
prevariety, 186
sheaf, 194
subvariety, 45
variety, 187
algebraically induced analytic sheaves, 347
aligned pair of boxes, 249
ample sheaf, 326
analytic modules of finite type, 487
analytic polyhedron, 261
analytic sheaf, 216
analytic vector, 486
Arens-Royden theorem, 296
Artin-Rees theorem, 197
balanced set, 264, 304
Banach algebra, 245, 288
bidegree of a differential form, 238
biholomorphic
equivalence, 51
mapping, 50, 55
biholomorphically equivalent, 56
biregular
mapping, 55
Borel subalgebra, 399, 443
Borel subgroup, 443
Borel-Weil theorem, 477
Borel-Weil-Bott theorem, 480
bounded
complex, 119
subset ofH(U), 30
bounded subset, 264
b o x i n C n , 249
branching order, 73
Cartan subalgebra, 395
Cartan's factorization lemma, 251
Cartan's first criterion, 391
Cartan's second criterion, 391
Cartan's Theorem A, 278
Cartan's Theorem B, 279
Cartan-Serre theorem, 302
Cartesian product
of prevarieties, 187
Casimir operator, 469
category, 114
abelian, 117
additive, 116
homotopy , 120
of functors, 115
of modules, 133
of morphisms, 115
Cauchy integral formula
generalized, 8
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