The endoscopic classification of representations: orthogonal and symplectic groups
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2013
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| Series: | American Mathematical Society colloquium publications
volume 61 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 590 Seiten |
| ISBN: | 9780821849903 |
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| 245 | 1 | 0 | |a The endoscopic classification of representations |b orthogonal and symplectic groups |c James Arthur |
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Record in the Search Index
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| adam_text | Titel: The endoscopic classification of representations
Autor: Arthur, James
Jahr: 2013
Contents
Foreword: A selective overview vii
Chapter 1. Parameters 1
1.1. The automorphic Langlands group 1
1.2. Self-dual, finite-dimensional representations 6
1.3. Representations of GL(N) 15
1.4. A substitute for global parameters 26
1.5. Statement of three main theorems 40
Chapter 2. Local Transfer 51
2.1. Langlands-Shelstad-Kottwitz transfer 51
2.2. Characterization of the local classification 62
2.3. Normalized intertwining operators 79
2.4. Statement of the local intertwining relation 96
2.5. Relations with Whittaker models 109
Chapter 3. Global Stabilization 121
3.1. The discrete part of the trace formula 121
3.2. Stabilization 130
3.3. Contribution of a parameter ip 138
3.4. A preliminary comparison 145
3.5. On the vanishing of coefficients 153
Chapter 4. The Standard Model 167
4.1. Statement of the stable multiplicity formula 167
4.2. On the global intertwining relation 173
4.3. Spectral terms 186
4.4. Endoscopic terms 193
4.5. The comparison 201
4.6. The two sign lemmas 214
4.7. On the global theorems 229
4.8. Remarks on general groups 240
Chapter 5. A Study of Critical Cases 253
5.1. The case of square integrable t/ 253
5.2. The case of elliptic ip 264
5.3. A supplementary parameter ip+ 272
5.4. Generic parameters with local constraints 286
VI CONTENTS
Chapter 6. The Local Classification 301
6.1. Local parameters 301
6.2. Construction of global representations k 309
6.3. Construction of global parameters j 321
6.4. The local intertwining relation for 332
6.5. Orthogonality relations for (j 346
6.6. Local packets for composite j 356
6.7. Local packets for simple (j 367
6.8. Resolution 377
Chapter 7. Local Nontempered Representations 387
7.1. Local parameters and duality 387
7.2. Construction of global parameters ip 396
7.3. The local intertwining relation for ip 404
7.4. Local packets for composite and simple ip 415
7.5. Some remarks on characters 429
Chapter 8. The Global Classification 443
8.1. On the final step 443
8.2. Proof by contradiction 453
8.3. Reflections on the results 469
8.4. Refinements of generic parameters for SO(2n) 485
8.5. An approximation of the regular part of Lp 503
Chapter 9. Inner Forms 513
9.1. Inner twists and automorphisms 513
9.2. Parameters and centralizers 526
9.3. On the normalization of transfer factors 536
9.4. Statement of the local classification 548
9.5. Statement of a global classification 560
Bibliography 572
Notations! Index 5g2
Subject Index 5gg
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:43:39Z |
| institution | BVB |
| isbn | 9780821849903 |
| language | English |
| lccn | 2013004694 |
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| physical | XVIII, 590 Seiten |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | American Mathematical Society |
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| series | American Mathematical Society colloquium publications |
| series2 | American Mathematical Society colloquium publications |
| spelling | Arthur, James 1944- Verfasser (DE-588)133218317 aut The endoscopic classification of representations orthogonal and symplectic groups James Arthur Providence, Rhode Island American Mathematical Society 2013 © 2013 XVIII, 590 Seiten txt rdacontent n rdamedia nc rdacarrier American Mathematical Society colloquium publications volume 61 Symplektische Gruppe (DE-588)4276585-7 gnd rswk-swf Orthogonale Gruppe (DE-588)4177508-9 gnd rswk-swf Orthogonale Gruppe (DE-588)4177508-9 s Symplektische Gruppe (DE-588)4276585-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-0969-2 American Mathematical Society colloquium publications volume 61 (DE-604)BV035417609 61 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026244045&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arthur, James 1944- The endoscopic classification of representations orthogonal and symplectic groups American Mathematical Society colloquium publications Symplektische Gruppe (DE-588)4276585-7 gnd Orthogonale Gruppe (DE-588)4177508-9 gnd |
| subject_GND | (DE-588)4276585-7 (DE-588)4177508-9 |
| title | The endoscopic classification of representations orthogonal and symplectic groups |
| title_auth | The endoscopic classification of representations orthogonal and symplectic groups |
| title_exact_search | The endoscopic classification of representations orthogonal and symplectic groups |
| title_full | The endoscopic classification of representations orthogonal and symplectic groups James Arthur |
| title_fullStr | The endoscopic classification of representations orthogonal and symplectic groups James Arthur |
| title_full_unstemmed | The endoscopic classification of representations orthogonal and symplectic groups James Arthur |
| title_short | The endoscopic classification of representations |
| title_sort | the endoscopic classification of representations orthogonal and symplectic groups |
| title_sub | orthogonal and symplectic groups |
| topic | Symplektische Gruppe (DE-588)4276585-7 gnd Orthogonale Gruppe (DE-588)4177508-9 gnd |
| topic_facet | Symplektische Gruppe Orthogonale Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026244045&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417609 |
| work_keys_str_mv | AT arthurjames theendoscopicclassificationofrepresentationsorthogonalandsymplecticgroups |