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Wallach N.R. — Real Reductive Groups II
Wallach N.R. — Real Reductive Groups II

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Название: Real Reductive Groups II

Автор: Wallach N.R.

Аннотация:

This book is the sequel to "Real Reductive Groups I", and emphasizes the more analytical aspects of representation theory, while still retaining its focus on the interaction between algebra, analysis and geometry, like the first volume. It provides a self-contained introduction to abstract representation theory, covering locally compact groups, C- algebras, Von Neuman algebras, direct integral decompositions. In addition, it contains a proof of Harish-Chandra's plancherel theorem. Together, the two volumes comprise a complete introduction to representation theory. Both volumes are based on courses and lectures given by the author over the last 20 years. They are intended for research mathematicians and graduate-level students taking courses in representation theory and mathematical physics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 454

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{\infty}$-vector      31
$\sigma$ algebra      358
($\mathfrak{g}$,K)-module      80
($\mathfrak{g}$,K)-module, equivalent      80
($\mathfrak{g}$,K)-module, finitely generated      80
($\mathfrak{g}$,K)-module, tempered      138
($\mathfrak{g}$,K)-module, underlying      81
Absolutely continuous measures      361
Adjacent parabolic subgroups      11
Admissible ($\mathfrak{g}$,K)-module      81
Admissible representation      81
Affine algebraic group      42
Algebraicly irreducible      287
Analytic vector      34
Approximate identity for ${L^1}(G)$      274
Approximate identity for C*-algebra      276
Approximate projection for a left ideal      277
AR (Artin-Rees) property      14
Augmentation homomorphism      9
Automorphic form      106
Banach *-algebra      268
Banach algebra      265
Borel set      359
Borel subalgebra      37
Bruhat decomposition      52
C*-algebra      268
C*-algebra of a locally compact group      274
Cartan decomposition, group      46
Cartan decomposition, Lie algebra      43
Cartan involution      42
Cartan subalgebra      4
Cartan subalgebra of a real Lie algebra      56
Cartan subalgebra, fundamental      57
Cartan subalgebra, maximally split      57
Cartan subgroup      59
Cartan subgroup, fundamental      59
Cartan subgroup, maximally split      59
Cartan — Helgason Theorem      51
CC(H)      292
CCR      299
Central distribution      294
Character (of a *-representation)      304
Chevalley restriction theorem      75
Clifford algebra      119
Coefficients (matrix)      22
Compact form      44
Constant term of a function      147
Constant term of a matrix coefficient      147
Cusp form, (for G)      233
Cusp form, (for G/N)      37
Decomposable operator      317
Dirac, inequality      368
Dirac, operator      368
Direct integral      314
Direct integral of representations      326
distribution      332
Distribution, character      292
Distribution, order      332
Double representation      216
Eisenstein integral      217
Essentially bounded function      360
Extreme subset of a convex set      289
Factor      329
Family of Hilbert spaces      312
Formal degree      24
Frobenius reciprocity      31
Functional equation for the Eisenstein integral      232
Functional equation for the Harish-Chandra C-function      232
Fundamental parabolic subgroup      248
Fundamental series      248
Gelfand transform      267
Gelfand — Naimark decomposition      54
Generalized weight space      108
Generic character (of $\mathbf{N}$)      371
GNS-construction      286
Harish-Chandra $\mu$ function      45
Harish-Chandra c-function      230
Harish-Chandra homomorphism      93
Harish-Chandra isomorphism      78
Harish-Chandra Schwartz space      230
Hilbert space, direct sum      314
Hilbert space, tensor product      356
Induced representation      31
Infinitesimal, character      34
Infinitesimal, equivalence      81
Infinitesimally irreducible      81
Integrable function      359
Intertwining operator, $\mathfrak{g}$-module      11
Intertwining operator, group representation      18
Isotypic component      28
Iwasawa decomposition, group      45
Iwasawa decomposition, Lie algebra      45
Jacobson topology      299
Jacquet integral      381
Jacquet module      111
Kaplansky density theorem      281
Langlands, data      149
Langlands, decomposition      51
Leading term      146
Liminaire      299
Locally integrable      332
Lower semi-continuous      305
Maass — Selberg relations      231
Maximal completion of moderate growth      84
Measurable ($\mu$) set      359
Measurable family of Hilbert spaces      312
Measure, Borel      359
Measure, complex Radon      361
Measure, Radon      360
Measure, regular Borel      360
Measure, space      359
Modular function      2
Nilpotent element      342
Norm      71
Operator field, measurable      317
Operator, compact      326
Operator, Hilbert — Schmidt      328
Operator, self-adjoint      326
Operator, trace class      328
P-B-W      9
Parabolic subgroup, minimal      51
Plancherel measure      341
Positive definite function      306
Positive element of a C*-algebra      271
Positive functional      284
Primitive ideal      298
Pure      289
Quantized Toda lattice      434
Quasi-compact      302
Rapidly decreasing function      230
Realization (of a ($\mathfrak{g}$,K)-module)      113
Representation of moderate growth      84
Representation, (strongly continuous of a) group      18
Representation, *-      271
Representation, conjugate dual      20
Representation, factorial      329
Representation, Hilbert      18
Representation, identity (of CC(H))      293
Representation, Lie algebra      11
Representation, nondegenerate      271
Representation, regular      22
Representation, smooth      18
Representation, square integrable      22
Representation, unitary      18
Representative of a Weyl group element      136
Schur orthogonality relations      23
Schur's Lemma Dixmier's      11
Schur's Lemma for ($\mathfrak{g}$,K)-modules      80
Schur's Lemma for groups      21
Schwartz space      237
Section, square integrable      312-313
Small representation      70
Smooth vector      31
Special vector subgroup      10
Spectral radius      266
Split component (standard)      48
State      289
Sterling's formula      55
Strong topology      280
Submersion      332
Symmetrization map      9
Tame functional (with respect to a p-pair)      368
TDS      11
Tempered Hilbert representation      144
Type 1      333
Ultra strong topology      293
Unipotent extension      80
Unitarily equivalent *-representations      272
Universal enveloping algebra      8
von Neumann algebra      319
von Neumann density theorem      279
Weak* topology      358
Weakly contained (in)      336
Weight, dominant integral      36
Weight, space      36
Weyl chamber      6 48
Weyl character formula      87
Weyl group      6
Weyl integration formula, Lie algebra      63
Weyl integration formula, Lie group      63
Weyl reflection      6
Whittaker transform      423
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