The Penrose transform: its interaction with representation theory
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1989
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 213 S. |
| ISBN: | 0198535651 |
Internformat
MARC
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| 100 | 1 | |a Baston, Robert J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Penrose transform |b its interaction with representation theory |c Robert J. Baston and Michael G. Eastwood |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1989 | |
| 300 | |a XV, 213 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford mathematical monographs | |
| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 7 | |a Penrose, transformation de |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 7 | |a Représentations de groupes |2 ram | |
| 650 | 7 | |a Torseurs, théorie des |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Penrose transform | |
| 650 | 4 | |a Representations of groups | |
| 650 | 4 | |a Twister theory | |
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| 700 | 1 | |a Eastwood, Michael G. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804117006064025600 |
|---|---|
| adam_text | CONTENTS
1 Introduction 1
Minkowski space 2
The Penrose transform 7
The Penrose transform on flag varieties 9
2 Lie Algebras and Flag Manifolds 10
2.1 Some structure theory 10
2.2 Borel and parabolic subalgebras 13
2.3 Generalized flag varieties 14
2.4 Fibrations of generalized flag varieties 18
3 Homogeneous Vector Bundles on GIP 21
3.1 A brief review of representation theory 21
3.2 Homogeneous bundles on GIP 28
3.3 A remark on inverse images 33
4 The Weyl Group, its Actions, and Hasse Diagrams 34
4.1 The Weyl Group 34
4.2 The affine Weyl action 39
4.3 The Hasse diagram of a parabolic subalgebra 39
4.4 Relative Hasse diagrams 43
5 The Bott Borel Weil Theorem 44
5.1 A simple proof 45
5.2 Some examples 48
5.3 Direct images 50
6 Realizations of GIP 53
6.1 The projective realization 55
6.2 The cell structure of GIP 56
6.3 Integral cohomology rings 58
6.4 Co Adjoint realizations and moment maps 61
7 The Penrose Transform in Principle 67
7.1 Pulling back cohomology 69
xiv CONTENTS
7.2 Pushing down cohomology 71
7.3 A spectral sequence 72
8 The Bernstein Gelfand Gelfand Resolution 74
8.1 A prototype 74
8.2 Translating BGG resolutions 78
8.3 The general case on GIB 79
8.4 The story for GIB 80
8.5 An algorithm for computation 83
8.6 Non standard morphisms 84
8.7 Relative BGG resolutions 85
9 The Penrose Transform in Practice 87
9.1 The homogeneous Penrose transform 89
9.2 The real thing 90
Positive helicity ZRM fields: k + 2 0 91
Negative helicity fields: k + 2 0 95
The scalar wave equation: k — 2 99
9.3 The Penrose transform of forms on twistor space 103
9.4 Other bundles on twistor space 105
Deformations and nonlinear gravitons 105
The Einstein bundle 106
9.5 The Penrose transform for ambitwistor space 107
9.6 Higher dimensions—conformal case 110
Zero rest mass fields in even dimensions 111
Zero rest mass fields in odd dimensions 115
9.7 A Grassmannian generalization 117
9.8 An exceptional example 123
9.9 The Ward correspondence 126
Background coupling 138
10 Constructing Unitary Representations 142
10.1 The discrete series of SU( 1,1) 142
10.2 Massless field representations 147
10.3 The twistor point of view 149
10.4 The twistor transform 154
10.5 Hermitian symmetric spaces 155
10.6 Towards discrete series 156
CONTENTS xv
11 Module Structures on Cohomology 158
11.1 Verma modules and differential operators 159
Verma modules 159
Relation to differential operators 160
Duals of Verma modules and jet sheaves 160
Elementary properties of Verma modules 162
Verma modules for other parabolics 163
11.2 Invariant differential operators 164
Characterization 164
Conformally invariant operators 165
General results 165
11.3 The algebraic Penrose transform 166
Categories of g modules and homogeneous sheaves 167
Algebraic equivalent of cohomology 167
The algebraic transform and Zuckerman functors 168
Dolbeault resolution and Fg 170
11.4 K types, local cohomolgy, and elementary states 171
Elementary states 172
g module structure on Haa 173
Local cohomology 174
Koszul complexes and local cohomology 177
Explicit hyperfunction representatives 180
^ types and Grothendieck duality 182
11.5 Homomorphisms of Verma modules 185
12 Conclusions and Outlook 191
Index 205
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:32Z |
| institution | BVB |
| isbn | 0198535651 |
| language | English |
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| physical | XV, 213 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
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| series2 | Oxford mathematical monographs |
| spelling | Baston, Robert J. Verfasser aut The Penrose transform its interaction with representation theory Robert J. Baston and Michael G. Eastwood Oxford Clarendon Press 1989 XV, 213 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Géométrie différentielle ram Penrose, transformation de ram Physique mathématique ram Représentations de groupes ram Torseurs, théorie des ram Mathematische Physik Geometry, Differential Mathematical physics Penrose transform Representations of groups Twister theory Penrose-Transformation (DE-588)4224816-4 gnd rswk-swf Penrose-Transformation (DE-588)4224816-4 s DE-604 Eastwood, Michael G. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001684913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baston, Robert J. Eastwood, Michael G. The Penrose transform its interaction with representation theory Géométrie différentielle ram Penrose, transformation de ram Physique mathématique ram Représentations de groupes ram Torseurs, théorie des ram Mathematische Physik Geometry, Differential Mathematical physics Penrose transform Representations of groups Twister theory Penrose-Transformation (DE-588)4224816-4 gnd |
| subject_GND | (DE-588)4224816-4 |
| title | The Penrose transform its interaction with representation theory |
| title_auth | The Penrose transform its interaction with representation theory |
| title_exact_search | The Penrose transform its interaction with representation theory |
| title_full | The Penrose transform its interaction with representation theory Robert J. Baston and Michael G. Eastwood |
| title_fullStr | The Penrose transform its interaction with representation theory Robert J. Baston and Michael G. Eastwood |
| title_full_unstemmed | The Penrose transform its interaction with representation theory Robert J. Baston and Michael G. Eastwood |
| title_short | The Penrose transform |
| title_sort | the penrose transform its interaction with representation theory |
| title_sub | its interaction with representation theory |
| topic | Géométrie différentielle ram Penrose, transformation de ram Physique mathématique ram Représentations de groupes ram Torseurs, théorie des ram Mathematische Physik Geometry, Differential Mathematical physics Penrose transform Representations of groups Twister theory Penrose-Transformation (DE-588)4224816-4 gnd |
| topic_facet | Géométrie différentielle Penrose, transformation de Physique mathématique Représentations de groupes Torseurs, théorie des Mathematische Physik Geometry, Differential Mathematical physics Penrose transform Representations of groups Twister theory Penrose-Transformation |
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