Авторизация
Поиск по указателям
Borel A., Mostow G.D. — Algebraic Groups and Discontinuous Subgroups: Proceedings
Обсудите книгу на научном форуме
Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: Algebraic Groups and Discontinuous Subgroups: Proceedings
Авторы: Borel A., Mostow G.D.
Аннотация: This book is an outgrowth of the twelfth Summer Mathematical Institute of the American Mathematical Society, which was devoted to Algebraic Groups and Discontinuous Subgroups. The Institute was held at the University of Colorado in Boulder from July S to August 6, 1965, and was financed by the National Science Foundation and the Office of Naval Research. The present volume consists of the Institute lecture notes, in part slightly revised, and of a few papers written somewhat later.
From the beginning, it was understood that a comprehensive exposition of the arithmetic aspects of algebraic groups should be a central aim of the Institute. In order to survey effectively the topics chosen for discussion, some important parts of the theory of Lie groups and algebraic groups had to be omitted, and the program was concentrated around five major themes: linear algebraic groups and arithmetic groups, adeles and arithmetic properties of algebraic groups, auto-morphic functions and spectral decomposition of
-spaces of coset spaces, holomorphic automorphic functions on bounded symmetric domains and moduli problems, vector valued cohomology and deformation of discrete subgroups. The lectures fulfilled diverse needs, and accordingly the papers in this book are intended to serve various purposes: to supply background material, to present the current status of a topic, to describe some basic methods, to give an exposition of more or less known material for which there is no convenient reference, and to present new results. It is hoped that this collection of papers will facilitate access to the subject and foster further progress.
Язык:
Рубрика: Математика /Алгебра /Теория групп /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1966
Количество страниц: 426
Добавлена в каталог: 26.03.2005
Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
-automorphic right spherical function 261
-function 291
-antihermitian form 317
-compactification, Satake 413 415
1-cocycle of 49
Abelian variety 312 313 315 316 318 338 345
Adelering 114
Adelized group 115
Adelized variety 114
Adjoint, group 38 42
Adjoint, representation 5
Admissible pair 72
Admissible PEL-structure 319
Affine algebraic group 4 5
Affine or extended Dynkin diagram 34
Affine Weyl group 35 68 74
Algebraic matrix group 3
Algebraic torus 7
Algebraic transformation group 5
Algebras L with a positive involution 319
Anisotropic, K-torus over 7
Anisotropic, kernels 39
Anisotropic, over K 7
Anisotropic, reductive groups 13
Anisotropic, reductive kernel 39
Anisotropic, semisimple kernel 47
Antihermitian form, - 317
Arithmetic groups 20 99 104
Automorphic factor 387
Automorphic form 200 201 204 326 391
Automorphism group 38
Automorphy, canonical factor 202 388 391 392
Automorphy, factor 201—203
BN-pair 71
Borel subgroup 11
Boundary components 287
Bounded subgroup 63
Bounded symmetric domain 319 320
Canonical automorphy factor 202 388 391 392
Canonical numbering 286
Cayley transforms, natural compacti-fications 285
Center 38
CHARACTER 6
Chevalley groups 143 148
Class, field 322
Class, numbers 188
Class, of -lattices 323
Classical groups 66
Cocycle of 49
Cohomologous, innerly 49
Cohomology, exact sequences in noncommutative 153
Cohomology, Galois 164 190 192
Cohomology, noncommutative 151 164
Commensurability subgroup of r 20
Compactification 281 292 284
Complex multiplication 320 322
Condition ( ) 352
Conjecture, Ramanujan and spherical functions 258
Conjecture, Ramanujan — Peterson 264
Conjugacy, Frobenius classes 267
Connected, simply algebraic group 154
Connected, simply covering 42
Connected, simply group 68
Connected, simply universal covering 38
Cusp-forms 222 226 230 233 331
Cusp-forms, spectral decomposition 225
Cylindrical sets 296
d-cohomology 398
d-cohomology, groups 394
d-cohomology, groups of vector valued forms 388
Decomposition, Jordan 6 26
Decomposition, spectral cusp-forms 225
Deformation of G-structure 407
Desingularization, problem of 301—303
Dimension, fields of 154
Discrete series 262
Discrete subgroups 268 272
Divisor, basic 314
Duality, Tate — Nakayama 127
Dynkin diagram 33—35 37 41 46 53
Eisenstein series 146 206 208 209 214 215 221 235 236 247 251 252
Eisenstein — Poincare series 284 285 291
Eisenstein — Siegel series 140
Element, R-regular 414
Euler product 327
Exact sequences 173
Exact sequences in noncommutative cohomology 153
Fibre, system of abelian varieties 323
Fibre, variety 326 327
Field of dimension 154
Field of moduli 282 321
Fock representation 381 363
Fourier — Jacobi series 288 296
Frobenius, conjugacy classes 267
Frobenius, reciprocity law 372
Fundamental set 21
Galois cohomology 164 190 192
Generalized Tits system 71 74 79
Harmonic theory 392
Hasse, principle for semisimple simply connected groups 155
Hasse, zeta-function 312
Hecke, algebra 79
Hecke, operators 326 327
Hecke, ring 78 79 326
Hermitian, mapping, (V-) 297
Hermitian, mapping, quasi- 288
Hermitian, modular group 283
Hillbert — Siegel modular group 282
Hillbert, group 358
Hillbert, modular forms 358—360
Hillbert, variety 358
Hodge group of a complex torus 347
Hodge group of an abelian variety 348
Homogeneous, principal space of a linear algebraic group 149
INDEX 39
Inner and outer form 39
Innerly cohomologous 49
Involution of an algebra 313
Involution, opposition 36
Isogenous, (strictly) over k or k-isogenous 34 42
Isogeny 34 313
Jordan decomposition 6 26
k or k-isogenous, strictly over 34 42
k representation strongly rational over 18
k roots 13
k split torus 7
k Weyl group relative to 13
k, anistropic torus over 7
k-primary 353
k-rank 13
L-functions 333 334
Laplace transform 212
Lattice 400
Lefschetz imbedding theorem 307 308
Lie algebra of an algebraic group 5
Linear algebraic groups 3
Locally trivial 389
Map, connecting 171
Map, G 406 408
Maximal family of polarized abelian varieties 315
Modular form 308
Modular function 212
Modular group, Hilbert — Siegel 282
Modular imbeddings 358—360
Moduli, variety 324
Moduli, variety for PEL-structures 321
Modulus, supersingular 265
Morphism of algebraic groups 5
Nakayama — Tate duality 127
Natural compactification 284 285
Natural compactification and Cayley transforms 285
Navier — Stokes equations 16 45 47 49
Nilpotent 9
Nilpotent, solvable algebraic group 8
Noncommutative cohomology 151 164
Noncommutative exact sequences in cohomology 153
Normal PEL-type 321 322
Opposition involution 36
Orbits, distinguished 39
Orthogonal group, special 107
Parabolic standard k -subgroups 14
Parabolic subgroup 9 38 41
Partial Cayley transformations 286
Partial desingularizations theorem 302 303
Pel-structure 347 318
PEL-structure, admissible 319
PEL-structure, moduli for 321
Pel-type 318
PEL-type, normal 321 322
Peterson — Ramanujan conjecture 264
Poincare series 204 205
Poincare — Eisenstein series 284 285 291
Polarization 306 314
Polarized Abelian variety 314
Polarized normally 282
Positive 313
Positive involution 316
Principal homogeneous space of a linear algebraic group, matrices 306
Principal homogeneous space of a linear algebraic group, series 211 261
Quaternion algebra, totally definite 319
Quaternion algebra, totally indefinite 319
Radical (of an algebraic group) 9
Ramanujan — Peterson conjecture 264
Ramanujan, conjecture and spherical functions 258
Rank of an algebraic group 10
Rank, k 13
Rational boundary components 284 289 290
Rational points 184
Rational representation 6
Reciprocity law, Frobenius 372
Reductive algebraic group 9
Reductive anistropic groups 13
Reductive anistropic kernel 39
Regular element 30
Relative Weyl group 40
Representation, adjoint 5
Representation, induced 370
Representation, infinitesimal 370
Representation, rational 6
Representation, special 275
Representation, strongly rational over k 18
Riemann, conditions 298 306
Riemann, form 313
Rigid at 407
Rigidity 418
Ring of Thetanullwerthe 309
Root, k 13
Root, system 11 12
s-semiautomorphism 176
Satake p-compactification 413 415
Schemes, semisimple group 99
Schrodinger representation 361
Semiautomorphism, s- 176
Semisimple algebraic group 9
Semisimple anistropic kernel 39
Semisimple element 414 416
Semisimple group schemes 99
Sequences, exact 173
Siegel — Eisenstein series 140
Siegel — Hilbert modular group 282
Siegel, domain 22—24 296
Siegel, formula 133 136 141 143
Siegel, modular form 358—360
Siegel, sets 297
Siegel, variety 358
SIMPLE 313
Simple almost 33
Singularity theorem 302 303
Solvable nilpotent algebraic group 8
Solvable split group 9
Spherical -automorphic right function 261
Spherical zonal function 258
Split, groups 66
Split, k-torus 7
Split, solvable group 9
Structure theorem 272
Supersingular 266 268
Supersingular, modulus 265
Supplementary series 261
Sylow subgroup 76
Symmetric domain 339
Symmetric domain, bounded 319 320
Symplectic pair 339
Symplectic representations 358
Tamagawa number 124 127 128 133
Tate, Nakayama-, duality 127
Tensor, twisted product 79
Tensor, twisted product, -function 311
Thetanullwerthe 308
Thetanullwerthe, ring of 309
Tits system 68 69 72
Tits system, (BN-pair) 71
Tits system, generalized 71 74 79
Tits system, saturated 72
Torus 68
Torus, algebraic 7
Torus, anistropic over k 7
Torus, split k- 7
Trace formula 329
Transform, Laplace 212
Transformation group, algebraic 5
Truncated domains 297
Truncated Siegel sets 290
Twisted highly 194
Twisted tensor product 79
Twisting 151
Unbounded realizations 285
Unimodular group 123
Unipotent 122
Unipotent, algebraic group 8
Unipotent, radical (of an algebraic group) 9
Unitary, special group 107
Variety, adelized 114
Vertices 34
Weight group 36
Weil’s conjecture 123 331
Weyl chamber 12 14 203 249
Weyl chamber, chamber 12 14 203 249
Weyl chamber, commutations relations 366
Weyl chamber, group 11 12 14 15 16 33 35 40 68 71 73 194 235 414
Weyl chamber, group, affine 35 68 74
Weyl chamber, group, extended 194
Weyl chamber, group, generalized 71
Weyl chamber, group, relative 40
Weyl chamber, group, relative to k 13 416
Zariski, dense 11 26
Zariski, density 104 105
Zeta function 329 331
Zeta function, Hasse 312
Zonal spherical function 258
Реклама