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Borel A., Mostow G.D. — Algebraic Groups and Discontinuous Subgroups: Proceedings
Borel A., Mostow G.D. — Algebraic Groups and Discontinuous Subgroups: Proceedings



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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 $L^2$-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: en

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
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Предметный указатель
$\Gamma$-automorphic right spherical function      261
$\mathfrak{U}$ -function      291
$\rho$-antihermitian form      317
$\rho$-compactification, Satake      413 415
1-cocycle of $\Gamma$      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, $\rho$-      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 $o_k$-lattices      323
Classical groups      66
Cocycle of $\Gamma$      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 ($H_1$)      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 $\infty$      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 $\Gamma$-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, $\theta$-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
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