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