Kac-Moody groups, their flag varieties and representation theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston u.a.
Birkhäuser
2002
|
| Series: | Progress in mathematics
204 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 606 S. |
| ISBN: | 0817642277 3764342277 |
Staff View
MARC
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| 100 | 1 | |a Kumar, Shrawan |d 1953- |e Verfasser |0 (DE-588)115543384 |4 aut | |
| 245 | 1 | 0 | |a Kac-Moody groups, their flag varieties and representation theory |c Shrawan Kumar |
| 246 | 1 | 3 | |a Kac Moody groups, their flag varieties and representation theory |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 2002 | |
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| 650 | 4 | |a Variétés de drapeaux (Géométrie) | |
| 650 | 4 | |a Flag manifolds | |
| 650 | 4 | |a Kac-Moody algebras | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Convention xiv
I. Kac Moody Algebras: Basic Theory 1
1. Definition of Kac Moody Algebras 2
2. Root Space Decomposition 5
3. Weyl Groups Associated to Kac Moody Algebras 11
4. Dominant Chamber and Tits Cone 27
5. Invariant Bilinear Form and the Casimir Operator 29
II. Representation Theory of Kac Moody Algebras 39
1. Category O 40
2. Weyl Kac Character Formula 47
3. Shapovalov Bilinear Form 51
III. Lie Algebra Homology and Cohomology 67
1. Basic Definitions and Elementary Properties 68
2. Lie Algebra Homology of n~:
Results of Kostant Garland Lepowsky 80
3. Decomposition of the Category O
and some Ext Vanishing Results 90
4. Laplacian Calculation 97
IV. An Introduction to ind Varieties and pro Groups 109
1. Ind Varieties: Basic Definitions 110
2. Ind Groups and their Lie Algebras 114
3. Smoothness of ind Varieties 122
4. An Introduction to pro Groups and pro Lie Algebras 129
V. Tits Systems: Basic Theory 149
1. An Introduction to Tits Systems 149
2. Refined Tits Systems 166
viii Contents
VI. Kac Moody Groups: Basic Theory 173
1. Definition of Kac Moody Groups and Parabolic Subgroups 174
2. Representations of Kac Moody Groups 187
VII. Generalized Flag Varieties of Kac Moody Groups 199
1. Generalized Flag Varieties: Ind Variety Structure 201
2. Line Bundles on XY 219
3. Study of the Group U~ 221
4. Study of the Group Qmin Defined by Kac Peterson 228
VIII. Demazure and Weyl Kac Character Formulas 245
1. Cohomology of Certain Line Bundles on Zro 246
2. Normality of Schubert Varieties
and the Demazure Character Formula 273
3. Extension of the Weyl Kac Character Formula
and the Borel Weil Bott Theorem 281
IX. BGG and Kempf Resolutions 295
1. BGG Resolution: Algebraic Proof in the Symmetrizable Case .. 297
2. A Combinatorial Description of the BGG Resolution 305
3. Kempf Resolution 321
X. Defining Equations of Q/V and Conjugacy Theorems 337
1. Quadratic Generation of Defining Ideals of Q/V
in Projective Embeddings 339
2. Conjugacy Theorems for Lie Algebras 347
3. Conjugacy Theorems for Groups 358
XI. Topology of Kac Moody Groups and Their Flag Varieties 369
1. The Nil Hecke Ring 371
2. Determination of R 392
3. T equivariant Cohomology of Q/B 396
4. Positivity of the Cup Product
in the Cohomology of Flag Varieties 416
5. Degeneracy of the Leray Serre Spectral Sequence
for the Fibration Qmin ? gâ„¢n/T 427
Contents ix
XII. Smoothness and Rational Smoothness of Schubert Varieties 447
1. Singular Locus of Schubert Varieties 449
2. Rational Smoothness of Schubert Varieties 465
XIII. An Introduction to Affine Kac Moody Lie Algebras and Groups 481
1. Affine Kac Moody Lie Algebras 482
2. Affine Kac Moody Groups 490
Appendix A. Results from Algebraic Geometry 511
Appendix B. Local Cohomology 527
Appendix C. Results from Topology 533
Appendix D. Relative Homological Algebra 539
Appendix E. An Introduction to Spectral Sequences 549
Bibliography 559
Index of Notation 591
Index 597
|
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:55:08Z |
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| isbn | 0817642277 3764342277 |
| language | English |
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| physical | XIII, 606 S. |
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| spelling | Kumar, Shrawan 1953- Verfasser (DE-588)115543384 aut Kac-Moody groups, their flag varieties and representation theory Shrawan Kumar Kac Moody groups, their flag varieties and representation theory Boston u.a. Birkhäuser 2002 XIII, 606 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 204 Kac-Moody, Algèbres de Lie-groepen gtt Représentations de groupes Variétés de drapeaux (Géométrie) Flag manifolds Kac-Moody algebras Representations of groups Fahnenmannigfaltigkeit (DE-588)4431550-8 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Kac-Moody-Gruppe (DE-588)4445639-6 gnd rswk-swf Kac-Moody-Gruppe (DE-588)4445639-6 s DE-604 Darstellung Mathematik (DE-588)4128289-9 s Fahnenmannigfaltigkeit (DE-588)4431550-8 s Progress in mathematics 204 (DE-604)BV000004120 204 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009553860&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kumar, Shrawan 1953- Kac-Moody groups, their flag varieties and representation theory Progress in mathematics Kac-Moody, Algèbres de Lie-groepen gtt Représentations de groupes Variétés de drapeaux (Géométrie) Flag manifolds Kac-Moody algebras Representations of groups Fahnenmannigfaltigkeit (DE-588)4431550-8 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Kac-Moody-Gruppe (DE-588)4445639-6 gnd |
| subject_GND | (DE-588)4431550-8 (DE-588)4128289-9 (DE-588)4445639-6 |
| title | Kac-Moody groups, their flag varieties and representation theory |
| title_alt | Kac Moody groups, their flag varieties and representation theory |
| title_auth | Kac-Moody groups, their flag varieties and representation theory |
| title_exact_search | Kac-Moody groups, their flag varieties and representation theory |
| title_full | Kac-Moody groups, their flag varieties and representation theory Shrawan Kumar |
| title_fullStr | Kac-Moody groups, their flag varieties and representation theory Shrawan Kumar |
| title_full_unstemmed | Kac-Moody groups, their flag varieties and representation theory Shrawan Kumar |
| title_short | Kac-Moody groups, their flag varieties and representation theory |
| title_sort | kac moody groups their flag varieties and representation theory |
| topic | Kac-Moody, Algèbres de Lie-groepen gtt Représentations de groupes Variétés de drapeaux (Géométrie) Flag manifolds Kac-Moody algebras Representations of groups Fahnenmannigfaltigkeit (DE-588)4431550-8 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Kac-Moody-Gruppe (DE-588)4445639-6 gnd |
| topic_facet | Kac-Moody, Algèbres de Lie-groepen Représentations de groupes Variétés de drapeaux (Géométrie) Flag manifolds Kac-Moody algebras Representations of groups Fahnenmannigfaltigkeit Darstellung Mathematik Kac-Moody-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009553860&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT kumarshrawan kacmoodygroupstheirflagvarietiesandrepresentationtheory |