Buildings and classical groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1997
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 373 S. graph.Darst. |
| ISBN: | 041206331X |
Internformat
MARC
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| 100 | 1 | |a Garrett, Paul |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Buildings and classical groups |c Paul Garrett |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1997 | |
| 300 | |a X, 373 S. |b graph.Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Algebraïsche groepen |2 gtt | |
| 650 | 7 | |a Groupes, Théorie des |2 ram | |
| 650 | 7 | |a Immeubles (Théorie des groupes) |2 ram | |
| 650 | 7 | |a Lineaire groepen |2 gtt | |
| 650 | 4 | |a Buildings (Group theory) | |
| 650 | 4 | |a Group theory | |
| 650 | 0 | 7 | |a Klassische Gruppe |0 (DE-588)4164040-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gebäude |g Mathematik |0 (DE-588)4123258-6 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Gebäude |g Mathematik |0 (DE-588)4123258-6 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007752376 | ||
Datensatz im Suchindex
| _version_ | 1804126040824479745 |
|---|---|
| adam_text | Contents
Introduction ix
1 Coxeter Groups 1
1.1 Words, lengths, presentations of groups 2
1.2 Coxeter groups, systems, diagrams 2
1.3 Reflections, roots 3
1.4 Roots and the length function 6
1.5 More on roots and lengths 9
1.6 Generalized reflections 11
1.7 Exchange, Deletion conditions 12
1.8 The Bruhat order 16
1.9 Special subgroups of Coxeter groups 20
2 Seven Infinite Families 25
2.1 Three spherical families 26
2.2 Four affine families 27
3 Chamber Complexes 31
3.1 Chamber complexes 32
3.2 The uniqueness lemma 35
3.3 Foldings, walls, reflections 36
3.4 Coxeter complexes 40
3.5 Characterization by foldings and walls 43
3.6 Corollaries.au foldings 48
4 Buildings .•, 51
,4.1 Apartments and.J)iildings: definitions 52
,4 2 Canonical retractions to apartments 53
4.3 Apartments ar Coxeter complexes 54
4.4,. Labels, links / 56
4.5 ^Convexity of apartments 59
4.6 Spherical buildings 59
5 BN pairs from Buildings 63
5.1 BN pairs: definitions 64
5.2 BN pairs from buildings 64
5.3 Parabolic (special) subgroups 70
5.4 Further Bruhat Tits decompositions 71
5.5 Generalized BN pairs 73
5.6 The spherical case 75
5.7 Buildings from BN pairs 79
6 Generic and Hecke Algebras 87
6.1 Generic algebras 88
6.2 Iwahori Hecke algebras 92
6.3 Generalized Iwahori Hecke algebras 95
7 Geometric Algebra 101
7.1 GL(n) (a prototype) 102
7.2 Bilinear and hermitian forms 106
7.3 Extendingisometries 111
7.4 Parabolics 114
8 Examples in Coordinates 119
8.1 Symplectic groups 120
8.2 Orthogonal groups O(n,n) 123
8.3 Orthogonal groups O(p,q) 125
8.4 Unitary groups in coordinates 127
9 Spherical Construction for GL(n) 131
9.1 Construction 132
9.2 Verification of the building axioms 132
9.3 Action of GL(n) on the building 136
9.4 The spherical BN pair in GL(n) 137
9.5 Analogous treatment of SL(n) 139
9.6 Symmetric groups as Coxeter groups 140
10 Spherical Construction for Isometry Groups 143
10.1 Constructions 144
10.2 Verification of the building axioms 145
10.3 The action of the isometry group 150
10.4 The spherical BN pair 151
10.5 Analogues for similitude groups 154
11 Spherical Oriflamme Complex 157
11.1 Oriflamme construction for SO(n,n) 158
11.2 Verification of the building axioms 159
11.3 The action of SO(n,n) 164
11.4 The spherical BN pair in SO(n,n) 168
11.5 Analogues for GO(n,n) 170
12 Reflections, Root Systems and Weyl Groups 173
12.1 Hyperplanes, chambers, walls 174
12.2 Reflection groups are Coxeter groups 177
12.3 Finite reflection groups 181
12.4 AfBne reflection groups 186
12.5 Affine Weyl groups 190
13 AfBne Coxeter Complexes 197
13.1 Tits cone model of Coxeter complexes 198
13.2 Positive definite (spherical) case 202
13.3 A lemma from Perron Frobenius 203
13.4 Local finiteness of Tits cones 205
13.5 Definition of geometric realizations 207
13.6 Criterion for affineness 209
13.7 The canonical metric 214
13.8 The seven infinite families 216
14 Affine Buildings 221
14.1 Affine buildings, trees: definitions 222
14.2 Canonical metrics on affine buildings 222
14.3 Negative curvature inequality 225
14.4 Contractibility 227
14.5 Completeness 228
14.6 Bruhat Tits fixed point theorem 229
14.7 Maximal compact subgroups 230
14.8 Special vertices, compact subgroups 235
15 Combinatorial Geometry 239
15.1 Minimal and reduced galleries 240
15.2 Characterizing apartments 241
15.3 Existence of prescribed galleries 242
15.4 Configurations of three chambers 244
15.5 Subsets of apartments 247
16 Spherical Building at Infinity 253
16.1 Sectors 254
16.2 Bounded subsets of apartments 255
16.3 Lemmas on isometries 256
16.4 Subsets of apartments 260
16.5 Configurations of chamber and sector 265
16.6 Sector and three chambers 267
16.7 Configurations of two sectors 270
16.8 Geodesic rays 274
16.9 The spherical building at infinity 277
16.10 Induced maps at infinity 284
17 Applications to Groups 289
17.1 Induced group actions at infinity 290
17.2 BN pairs, parahorics and parabolics 291
17.3 Translations and Levi components 293
17.4 Levi filtration by sectors 294
17.5 Bruhat and Cartan decompositions 297
17.6 Iwasawa decomposition 297
17.7 Maximally strong transitivity 299
17.8 Canonical translations 301
18 Lattices, p adic Numbers, Discrete Valuations 305
18.1 p adic numbers 306
18.2 Discrete valuations 309
18.3 Hensel s Lemma 311
18.4 Lattices 313
18.5 Some topology 314
18.6 Iwahori decomposition for GL(n,k) 317
19 Affine Building for SL(n) 321
19.1 Construction 322
19.2 Verification of the building axioms 324
19.3 The action of SL(V) 329
19.4 The Iwahori subgroup B 330
19.5 The maximal apartment system 332
20 Affine Buildings for Isometry Groups 335
20.1 Affine buildings for alternating spaces 336
20.2 The double oriflamme complex 338
20.3 The (affine) single oriflamme complex 340
20.4 Verification of the building axioms 344
20.5 Group actions on the buildings 347
20.6 Iwahori subgroups 349
20.7 The maximal apartment systems 351
Bibliography 353
Index 371
|
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| author | Garrett, Paul |
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| ctrlnum | (OCoLC)37011543 (DE-599)BVBBV011520508 |
| dewey-full | 512.202462 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.202462 |
| dewey-search | 512.202462 |
| dewey-sort | 3512.202462 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV011520508 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:08Z |
| institution | BVB |
| isbn | 041206331X |
| language | English |
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| physical | X, 373 S. graph.Darst. |
| publishDate | 1997 |
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| publisher | Chapman & Hall |
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| spelling | Garrett, Paul Verfasser aut Buildings and classical groups Paul Garrett 1. ed. London [u.a.] Chapman & Hall 1997 X, 373 S. graph.Darst. txt rdacontent n rdamedia nc rdacarrier Algebraïsche groepen gtt Groupes, Théorie des ram Immeubles (Théorie des groupes) ram Lineaire groepen gtt Buildings (Group theory) Group theory Klassische Gruppe (DE-588)4164040-8 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gebäude Mathematik (DE-588)4123258-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Gebäude Mathematik (DE-588)4123258-6 s Klassische Gruppe (DE-588)4164040-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007752376&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garrett, Paul Buildings and classical groups Algebraïsche groepen gtt Groupes, Théorie des ram Immeubles (Théorie des groupes) ram Lineaire groepen gtt Buildings (Group theory) Group theory Klassische Gruppe (DE-588)4164040-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Gebäude Mathematik (DE-588)4123258-6 gnd |
| subject_GND | (DE-588)4164040-8 (DE-588)4072157-7 (DE-588)4123258-6 |
| title | Buildings and classical groups |
| title_auth | Buildings and classical groups |
| title_exact_search | Buildings and classical groups |
| title_full | Buildings and classical groups Paul Garrett |
| title_fullStr | Buildings and classical groups Paul Garrett |
| title_full_unstemmed | Buildings and classical groups Paul Garrett |
| title_short | Buildings and classical groups |
| title_sort | buildings and classical groups |
| topic | Algebraïsche groepen gtt Groupes, Théorie des ram Immeubles (Théorie des groupes) ram Lineaire groepen gtt Buildings (Group theory) Group theory Klassische Gruppe (DE-588)4164040-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Gebäude Mathematik (DE-588)4123258-6 gnd |
| topic_facet | Algebraïsche groepen Groupes, Théorie des Immeubles (Théorie des groupes) Lineaire groepen Buildings (Group theory) Group theory Klassische Gruppe Gruppentheorie Gebäude Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007752376&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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