Nilpotent orbits in semisimple lie algebras:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Van Nostrand Reinhold
1993
|
| Series: | Mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 186 S. graph. Darst. |
| ISBN: | 0534188346 |
Staff View
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| 100 | 1 | |a Collingwood, David H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nilpotent orbits in semisimple lie algebras |c David H. Collingwood ; William M. McGovern |
| 264 | 1 | |a New York |b Van Nostrand Reinhold |c 1993 | |
| 300 | |a XIII, 186 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Preliminaries 1
1.1 Nilpotent and Semisimple Elements 1
1.2 Adjoint Orbits 5
1.3 Coadjoint Orbits 11
1.4 Orbits as Symplectic Manifolds 15
2 Semisimple Orbits 19
2.1 Some Structure Theory 19
2.2 Classification of Semisimple Orbits 24
2.3 Basic Topology of Semisimple Orbits 28
3 The Dynkin Kostant Classification 29
3.1 Type An 30
3.2 Strategy 32
3.3 The Jacobson Morozov Theorem 37
3.4 Theorems of Kostant and Mal cev 40
3.5 Weighted Dynkin Diagrams 45
xi
xii Contents
3.6 Weighted Dynkin Diagrams for Type An 47
3.7 Centralizer Structure 49
3.8 Parabolic Subalgebras 51
4 Principal, Subregular, and Minimal
Nilpotent Orbits 55
4.1 The Principal Nilpotent Orbit 56
4.2 The Subregular Nilpotent Orbit 59
4.3 The Minimal Nilpotent Orbit 61
4.4 The Exponents of a Semisimple Group 64
5 Nilpotent Orbits in the
Classical Algebras 69
5.1 Partition Type Classifications 69
5.2 Explicit Standard Triples 74
5.3 Weighted Dynkin Diagrams 80
5.4 Partitions Corresponding to Oprin, O8Ubreg, and Omin 85
6 Topology of Nilpotent Orbits 87
6.1 The Fundamental Group and A(O) 87
6.2 The Closure Ordering 93
6.3 Special Nilpotent Orbits in the Classical Algebras 97
7 Induced Nilpotent Orbits 105
7.1 Basic Results 105
7.2 Induced Nilpotent Orbits in Type A 110
Contents xiii
7.3 Induced and Rigid Orbits in the Classical Algebras 113
8 The Exceptional Cases and
Bala Carter Theory 119
8.1 Levi Subalgebras Containing Nilpotent Elements 119
8.2 Distinguished Nilpotent Elements and Parabolic
Subalgebras 121
8.3 Connections with Induction 126
8.4 Tables 127
9 Real Nilpotent Orbits 135
9.1 Survey of Real Simple Algebras 135
9.2 The Jacobson Morozov Theorem Revisited 137
9.3 Nilpotent Orbits in Classical Algebras 139
9.4 Cayley and Normal Triples: Basic Conjugacy Results 145
9.5 Sekiguchi s Bijection and Weighted Dynkin Diagrams 147
9.6 Tables of the Real Exceptional Orbits 150
10 Advanced Topics 165
10.1 The Springer Correspondence 165
10.2 Associated Varieties of Primitive Ideals 170
10.3 Classification of Primitive Ideals 172
10.4 Primitive Ideals and the Geometry of Orbits 175
Bibliography 179
Index 184
|
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| author | Collingwood, David H. McGovern, William M. 1959- |
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| id | DE-604.BV008196128 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:08Z |
| institution | BVB |
| isbn | 0534188346 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005408298 |
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| owner_facet | DE-12 DE-739 DE-824 DE-29T DE-703 DE-11 DE-188 |
| physical | XIII, 186 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Van Nostrand Reinhold |
| record_format | marc |
| series2 | Mathematics series |
| spelling | Collingwood, David H. Verfasser aut Nilpotent orbits in semisimple lie algebras David H. Collingwood ; William M. McGovern New York Van Nostrand Reinhold 1993 XIII, 186 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics series Lie, algèbres de ram Orbites, méthode des ram Lie algebras Orbit method Halbeinfache Lie-Algebra (DE-588)4193986-4 gnd rswk-swf Nilpotenter Orbit (DE-588)4304229-6 gnd rswk-swf Nilpotenter Orbit (DE-588)4304229-6 s Halbeinfache Lie-Algebra (DE-588)4193986-4 s DE-604 McGovern, William M. 1959- Verfasser (DE-588)124769179 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005408298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Collingwood, David H. McGovern, William M. 1959- Nilpotent orbits in semisimple lie algebras Lie, algèbres de ram Orbites, méthode des ram Lie algebras Orbit method Halbeinfache Lie-Algebra (DE-588)4193986-4 gnd Nilpotenter Orbit (DE-588)4304229-6 gnd |
| subject_GND | (DE-588)4193986-4 (DE-588)4304229-6 |
| title | Nilpotent orbits in semisimple lie algebras |
| title_auth | Nilpotent orbits in semisimple lie algebras |
| title_exact_search | Nilpotent orbits in semisimple lie algebras |
| title_full | Nilpotent orbits in semisimple lie algebras David H. Collingwood ; William M. McGovern |
| title_fullStr | Nilpotent orbits in semisimple lie algebras David H. Collingwood ; William M. McGovern |
| title_full_unstemmed | Nilpotent orbits in semisimple lie algebras David H. Collingwood ; William M. McGovern |
| title_short | Nilpotent orbits in semisimple lie algebras |
| title_sort | nilpotent orbits in semisimple lie algebras |
| topic | Lie, algèbres de ram Orbites, méthode des ram Lie algebras Orbit method Halbeinfache Lie-Algebra (DE-588)4193986-4 gnd Nilpotenter Orbit (DE-588)4304229-6 gnd |
| topic_facet | Lie, algèbres de Orbites, méthode des Lie algebras Orbit method Halbeinfache Lie-Algebra Nilpotenter Orbit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005408298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT collingwooddavidh nilpotentorbitsinsemisimpleliealgebras AT mcgovernwilliamm nilpotentorbitsinsemisimpleliealgebras |