The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2008
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
896 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Volume 192, number 875 (first of 5 numbers)" Includes bibliographical references |
| Beschreibung: | VII, 83 S. graph. Darst. |
| ISBN: | 9780821840542 |
Internformat
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| 100 | 1 | |a Kapovich, Michael |d 1963- |e Verfasser |0 (DE-588)134100409 |4 aut | |
| 245 | 1 | 0 | |a The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |c Michael Kapovich ; Bernhard Leeb ; John J. Millson |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2008 | |
| 300 | |a VII, 83 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 896 | |
| 500 | |a "Volume 192, number 875 (first of 5 numbers)" | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Semisimple Lie groups | |
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 4 | |a Geometric group theory | |
| 650 | 4 | |a Lorentz groups | |
| 650 | 4 | |a Symmetric spaces | |
| 650 | 4 | |a Rings (Algebra) | |
| 650 | 0 | 7 | |a Polygon |0 (DE-588)4175197-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Symmetrischer Raum |0 (DE-588)4184206-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Leeb, Bernhard |e Sonstige |4 oth | |
| 700 | 1 | |a Millson, John James |e Sonstige |4 oth | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 896 |w (DE-604)BV008000141 |9 896 | |
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Datensatz im Suchindex
| _version_ | 1804137498517962752 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
Chapter 2. Roots and Coxeter Groups 7
2.1. Split tori over F 7
2.2. Roots, coroots and the Langlands dual 8
2.3. Coxeter groups 9
Chapter 3. The First_Three Algebra Problems and the Parameter Spaces E
for K G/K 12
3.1. The generalized eigenvalues of a sum problem Ql and the parameter
space £ of if-double cosets 13
3.2. The generalized singular values of a product and the parameter space
£ of if-double cosets 13
3.3. The generalized invariant factor problem and the parameter space E
of if-double cosets 14
3.4. Comparison of the parameter spaces for the four algebra problems 16
3.5. Linear algebra problems 16
Chapter 4. The existence of polygonal linkages and solutions to the algebra
problems 19
4.1. Setting up the general geometry problem 19
4.2. Geometries modeled on Coxeter complexes 21
4.3. Bruhat-Tits buildings associated with nonarchimedean reductive Lie
groups 24
4.4. Geodesic polygons 25
Chapter 5. Weighted Configurations, Stability and the Relation to Polygons 29
5.1. Gauss maps and associated dynamical systems 30
5.2. The polyhedron Dn(X) 33
5.3. The polyhedron for the root system B2 35
Chapter 6. Polygons in Euclidean Buildings and the Generalized Invariant
Factor Problem 37
6.1. Folding polygons into apartments 37
6.2. A Solution of Problem Q2 is not necessarily a solution
of Problem Q3 40
Chapter 7. The Existence of Fixed Vertices in Buildings and Computation of
the Saturation Factors for Reductive Groups 45
7.1. The saturation factors associated to a root system 45
7.2. The existence of fixed vertices 50
v
vi CONTENTS
7.3. Saturation factors for reductive groups 56
Chapter 8. The Comparison of Problems Q3 and Q4 60
8.1. The Hecke ring 60
8.2. A geometric interpretation of mO]^7(0) 62
8.3. The Satake transform 64
8.4. A solution of Problem Q4 is a solution of Problem Q3 67
8.5. A Solution of Problem Q3 is not necessarily
a solution of Problem Q4 71
8.6. The saturation theorem for GL(l) 73
8.7. Computations for the root systems £?2 and C?2 75
Appendix A. Decomposition of Tensor Products
and Mumford Quotients of Products of Coadjoint orbits 77
A.I. The existence of semistable triples and nonzero invariant vectorsin
triple tensor products 77
A.2. The semigroups of solutions to Problems Ql and Q4 80
Bibliography 82
|
| adam_txt |
Contents
Chapter 1. Introduction 1
Chapter 2. Roots and Coxeter Groups 7
2.1. Split tori over F 7
2.2. Roots, coroots and the Langlands' dual 8
2.3. Coxeter groups 9
Chapter 3. The First_Three Algebra Problems and the Parameter Spaces E
for K\G/K 12
3.1. The generalized eigenvalues of a sum problem Ql and the parameter
space £ of if-double cosets 13
3.2. The generalized singular values of a product and the parameter space
£ of if-double cosets 13
3.3. The generalized invariant factor problem and the parameter space E
of if-double cosets 14
3.4. Comparison of the parameter spaces for the four algebra problems 16
3.5. Linear algebra problems 16
Chapter 4. The existence of polygonal linkages and solutions to the algebra
problems 19
4.1. Setting up the general geometry problem 19
4.2. Geometries modeled on Coxeter complexes 21
4.3. Bruhat-Tits buildings associated with nonarchimedean reductive Lie
groups 24
4.4. Geodesic polygons 25
Chapter 5. Weighted Configurations, Stability and the Relation to Polygons 29
5.1. Gauss maps and associated dynamical systems 30
5.2. The polyhedron Dn(X) 33
5.3. The polyhedron for the root system B2 35
Chapter 6. Polygons in Euclidean Buildings and the Generalized Invariant
Factor Problem 37
6.1. Folding polygons into apartments 37
6.2. A Solution of Problem Q2 is not necessarily a solution
of Problem Q3 40
Chapter 7. The Existence of Fixed Vertices in Buildings and Computation of
the Saturation Factors for Reductive Groups 45
7.1. The saturation factors associated to a root system 45
7.2. The existence of fixed vertices 50
v
vi CONTENTS
7.3. Saturation factors for reductive groups 56
Chapter 8. The Comparison of Problems Q3 and Q4 60
8.1. The Hecke ring 60
8.2. A geometric interpretation of mO]^7(0) 62
8.3. The Satake transform 64
8.4. A solution of Problem Q4 is a solution of Problem Q3 67
8.5. A Solution of Problem Q3 is not necessarily
a solution of Problem Q4 71
8.6. The saturation theorem for GL(l) 73
8.7. Computations for the root systems £?2 and C?2 75
Appendix A. Decomposition of Tensor Products
and Mumford Quotients of Products of Coadjoint orbits 77
A.I. The existence of semistable triples and nonzero invariant vectorsin
triple tensor products 77
A.2. The semigroups of solutions to Problems Ql and Q4 80
Bibliography 82 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:13:30Z |
| indexdate | 2024-07-09T21:13:15Z |
| institution | BVB |
| isbn | 9780821840542 |
| language | English |
| lccn | 2007060581 |
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| physical | VII, 83 S. graph. Darst. |
| publishDate | 2008 |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Kapovich, Michael 1963- Verfasser (DE-588)134100409 aut The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra Michael Kapovich ; Bernhard Leeb ; John J. Millson Providence, RI American Mathematical Society 2008 VII, 83 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 896 "Volume 192, number 875 (first of 5 numbers)" Includes bibliographical references Semisimple Lie groups Linear algebraic groups Geometric group theory Lorentz groups Symmetric spaces Rings (Algebra) Polygon (DE-588)4175197-8 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 s Polygon (DE-588)4175197-8 s DE-604 Leeb, Bernhard Sonstige oth Millson, John James Sonstige oth Memoirs of the American Mathematical Society 896 (DE-604)BV008000141 896 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kapovich, Michael 1963- The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra Memoirs of the American Mathematical Society Semisimple Lie groups Linear algebraic groups Geometric group theory Lorentz groups Symmetric spaces Rings (Algebra) Polygon (DE-588)4175197-8 gnd Symmetrischer Raum (DE-588)4184206-6 gnd |
| subject_GND | (DE-588)4175197-8 (DE-588)4184206-6 |
| title | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |
| title_auth | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |
| title_exact_search | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |
| title_exact_search_txtP | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |
| title_full | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra Michael Kapovich ; Bernhard Leeb ; John J. Millson |
| title_fullStr | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra Michael Kapovich ; Bernhard Leeb ; John J. Millson |
| title_full_unstemmed | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra Michael Kapovich ; Bernhard Leeb ; John J. Millson |
| title_short | The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |
| title_sort | the generalized triangle inequalities in symmetric spaces and buildings with applications to algebra |
| topic | Semisimple Lie groups Linear algebraic groups Geometric group theory Lorentz groups Symmetric spaces Rings (Algebra) Polygon (DE-588)4175197-8 gnd Symmetrischer Raum (DE-588)4184206-6 gnd |
| topic_facet | Semisimple Lie groups Linear algebraic groups Geometric group theory Lorentz groups Symmetric spaces Rings (Algebra) Polygon Symmetrischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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