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Wallach N.R. — Real Reductive Groups II
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Название: Real Reductive Groups IIАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1992Количество страниц: 454Добавлена в каталог: 31.10.2010Операции: Положить на полку |
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31 358 ( 80 ( 80 ( 80 ( 138 ( 81 Absolutely continuous measures 361 Adjacent parabolic subgroups 11 Admissible ( 81 Admissible representation 81 Affine algebraic group 42 Algebraicly irreducible 287 Analytic vector 34 Approximate identity for 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 371 GNS-construction 286 Harish-Chandra 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, 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 ( 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 ( 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 ( 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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