Continuous cohomology, discrete subgroups, and representations of reductive groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2000]
|
| Edition: | Second edition |
| Series: | Mathematical surveys and monographs
volume 67 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 260 Seiten |
| ISBN: | 9781470412258 0821808516 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Introduction to the First Edition xi
Introduction to the Second Edition xvii
Chapter 0. Notation and Preliminaries 1
1. Notation 1
2. Representations of Lie groups 2
3. Linear algebraic and reductive groups 4
Chapter I. Relative Lie Algebra Cohomology 7
1. Lie algebra cohomology 7
2. The Ext functors for (g, t) modules 9
3. Long exact sequences and Ext 13
4. A vanishing theorem 15
5. Extension to (g, ii j modules 16
6. (g, 6, L) modules.
A Hochschild Serre spectral sequence in the relative case 19
7. Poincare duality 22
8. The Zuckerman functors 25
Chapter II. Scalar Product, Laplacian and Casimir Element 31
1. Notation and general remarks 31
2. Scalar product 33
3. Special cases 36
4. The bigrading in the bounded symmetric domain case 37
5. Cohomology with respect to square integrable representations 40
6. Spinors and the spin Laplacian 43
7. Vanishing theorems using spinors 47
8. Matsushima s vanishing theorem 50
9. Direct products 54
10. Sharp vanishing theorems 55
Chapter III. Cohomology with Respect to an Induced Representation 59
1. Notation and conventions 59
2. Induced representations and their K finite vectors 61
3. Cohomology with respect to principal series representations 64
4. Fundamental parabolic subgroups 66
5. Tempered representations 69
6. Representations induced from tempered ones 70
7. Appendix: Cx vectors in certain induced representations 70
vii
viii CONTENTS
Chapter IV. The Langlands Classification and Uniformly Bounded
Representations 75
1. Some results of Harish Chandra 75
2. Some ideas of Casselman 78
3. The Langlands classification (first step) 81
4. The Langlands classification (second step) 84
5. A necessary condition for uniform boundedness 87
6. Appendix: Langlands geometric lemmas 91
7. Appendix: A lemma on exponential polynomial series 94
Chapter V. Cohomology with Coefficients in HX(G) 97
1. Preliminaries 97
2. The class 11^ (G) 100
3. A vanishing theorem for the class LT^o(G) 100
4. Cohomology with coefficients in the Steinberg representation 103
5. Hl and the topology of S(G) 107
6. A more detailed examination of first cohomology 110
Chapter VI. The Computation of Certain Cohomology Groups 115
0. Translation functors 115
1. Cohomology with respect to minimal
non tempered representations. I 117
2. Cohomology with respect to minimal
non tempered representations. II 120
3. Semi simple Lie groups with R rank 1 122
4. The groups SO(n, 1) and SU(n, 1) 127
5. The Vogan Zuckerman theorem 134
Chapter VII. Cohomology of Discrete Subgroups and Lie Algebra
Cohomology 137
1. Manifolds 137
2. Discrete subgroups 139
3. F cocompact, E a unitary F module 142
4. G semi simple, T cocompact, E a unitary F module 145
5. F cocompact, E a G module 147
6. G semi simple, T cocompact, E a G module 149
Chapter VIII. The Construction of Certain Unitary Representations and
the Computation of the Corresponding Cohomology Groups 151
1. The oscillator representation 151
2. The decomposition of the restriction of the
oscillator representation to certain subgroups 155
3. The theta distributions 161
4. The reciprocity formula 164
5. The imbedding of Vi into L2(r G) 165
Chapter IX. Continuous Cohomology and Differentiable Cohomology 169
Introduction 169
1. Continuous cohomology for locally compact groups 170
2. Shapiro s lemma 175
CONTENTS ix
3. Hausdorff cohomology 177
4. Spectral sequences 178
5. Differentiable cohomology
and continuous cohomology for Lie groups 180
6. Further results on differentiable cohomology 184
Chapter X. Continuous and Differentiable Cohomology
for Locally Compact Totally Disconnected Groups 191
1. Continuous and smooth cohomology 191
2. Cohomology of reductive groups and buildings 196
3. Representations of reductive groups 199
4. Cohomology with respect to
irreducible admissible representations 200
5. Forgetting the topology 205
6. Cohomology of products 207
Chapter XL Cohomology with Coefficients in IIOC(G): The p adic Case 211
1. Some results of Harish Chandra 211
2. The Langlands classification (p adic case) 215
3. Uniformly bounded representations and noc(G) 218
4. Another proof of the non unitarizability of the Vj s 221
Chapter XII. Differentiable Cohomology for
Products of Real Lie Groups and T.D. Groups 225
0. Homological algebra over idempotented algebras 225
1. Differentiable cohomology 226
2. Modules of /f finite vectors 228
3. Cohomology of products 230
Chapter XIII. Cohomology of Discrete Cocompact Subgroups 233
1. Subgroups of products of Lie groups and t.d. groups 233
2. Products of reductive groups 236
3. Irreducible subgroups of semi simple groups 239
4. The F module E is the restriction of a rational G module 243
Chapter XIV. Non cocompact 5 arithmetic Subgroups 247
1. General properties 247
2. Stable cohomology 247
3. The use of L2 cohomology 249
4. 5 arithmetic subgroups 251
Bibliography 253
Index 259
|
| any_adam_object | 1 |
| author | Borel, Armand 1923-2003 Wallach, Nolan R. 1940- |
| author_GND | (DE-588)119089106 (DE-588)133231690 |
| author_facet | Borel, Armand 1923-2003 Wallach, Nolan R. 1940- |
| author_role | aut aut |
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| author_variant | a b ab n r w nr nrw |
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| callnumber-first | Q - Science |
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| classification_rvk | SI 830 SK 340 SK 320 |
| ctrlnum | (OCoLC)39875244 (DE-599)BVBBV019687392 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV019687392 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:03:50Z |
| institution | BVB |
| isbn | 9781470412258 0821808516 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013015257 |
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| owner_facet | DE-355 DE-BY-UBR DE-29T DE-11 |
| physical | xvii, 260 Seiten |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Borel, Armand 1923-2003 Verfasser (DE-588)119089106 aut Continuous cohomology, discrete subgroups, and representations of reductive groups A. Borel, N. Wallach Second edition Providence, Rhode Island American Mathematical Society [2000] © 2000 xvii, 260 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 67 Homologie ram Lie, Groupes de ram Représentations de groupes ram Homology theory Lie groups Representations of groups Stetige Kohomologie (DE-588)4183163-9 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Diskrete Untergruppe (DE-588)4257236-8 gnd rswk-swf Reduktive Gruppe (DE-588)4177313-5 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Diskrete Untergruppe (DE-588)4257236-8 s DE-604 Stetige Kohomologie (DE-588)4183163-9 s Reduktive Gruppe (DE-588)4177313-5 s Darstellungstheorie (DE-588)4148816-7 s Darstellung Mathematik (DE-588)4128289-9 s Lie-Gruppe (DE-588)4035695-4 s b DE-604 Wallach, Nolan R. 1940- Verfasser (DE-588)133231690 aut Erscheint auch als Online-Ausgabe 978-1-4704-1294-4 Mathematical surveys and monographs volume 67 (DE-604)BV000018014 67 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013015257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borel, Armand 1923-2003 Wallach, Nolan R. 1940- Continuous cohomology, discrete subgroups, and representations of reductive groups Mathematical surveys and monographs Homologie ram Lie, Groupes de ram Représentations de groupes ram Homology theory Lie groups Representations of groups Stetige Kohomologie (DE-588)4183163-9 gnd Lie-Gruppe (DE-588)4035695-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd Diskrete Untergruppe (DE-588)4257236-8 gnd Reduktive Gruppe (DE-588)4177313-5 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| subject_GND | (DE-588)4183163-9 (DE-588)4035695-4 (DE-588)4148816-7 (DE-588)4257236-8 (DE-588)4177313-5 (DE-588)4128289-9 |
| title | Continuous cohomology, discrete subgroups, and representations of reductive groups |
| title_auth | Continuous cohomology, discrete subgroups, and representations of reductive groups |
| title_exact_search | Continuous cohomology, discrete subgroups, and representations of reductive groups |
| title_full | Continuous cohomology, discrete subgroups, and representations of reductive groups A. Borel, N. Wallach |
| title_fullStr | Continuous cohomology, discrete subgroups, and representations of reductive groups A. Borel, N. Wallach |
| title_full_unstemmed | Continuous cohomology, discrete subgroups, and representations of reductive groups A. Borel, N. Wallach |
| title_short | Continuous cohomology, discrete subgroups, and representations of reductive groups |
| title_sort | continuous cohomology discrete subgroups and representations of reductive groups |
| topic | Homologie ram Lie, Groupes de ram Représentations de groupes ram Homology theory Lie groups Representations of groups Stetige Kohomologie (DE-588)4183163-9 gnd Lie-Gruppe (DE-588)4035695-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd Diskrete Untergruppe (DE-588)4257236-8 gnd Reduktive Gruppe (DE-588)4177313-5 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| topic_facet | Homologie Lie, Groupes de Représentations de groupes Homology theory Lie groups Representations of groups Stetige Kohomologie Lie-Gruppe Darstellungstheorie Diskrete Untergruppe Reduktive Gruppe Darstellung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013015257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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