Rational representations of algebraic groups: tensor products and filtrations
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
[1985]
|
| Series: | Lecture notes in mathematics
1140 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 253 Seiten |
| ISBN: | 3540156682 0387156682 |
Staff View
MARC
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| 100 | 1 | |a Donkin, Stephen |d 1953- |0 (DE-588)1210724472 |4 aut | |
| 245 | 1 | 0 | |a Rational representations of algebraic groups |b tensor products and filtrations |c Stephen Donkin |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c [1985] | |
| 264 | 4 | |c © 1985 | |
| 300 | |a VII, 253 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1140 | |
| 650 | 7 | |a Algebraïsche groepen |2 gtt | |
| 650 | 4 | |a Groupes linéaires algébriques | |
| 650 | 4 | |a Représentations de groupes | |
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 4 | |a Representations of groups | |
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| 650 | 0 | 7 | |a Filtration |0 (DE-588)4017164-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
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Table of Contents
introduction 1
Chapter 1. Homological algebra 7
1.1 Induction 7
1.2 Injective modules for soluble groups 12
1.3 Reductive groups 14
1.4 B cohomology 15
1.5 Induced modules 16
1.6 Kempf's Vanishing Theorem 18
1.7 Parabolic subgroups 18
Chapter 2. More homological algebra 21
2.1 Applications of the Vanishing Theorem 21
2.2 Euler characteristics 22
2.3 Some useful results 26
Chapter 3. Reductions 31
3.1 Good filtrations 31
3.2 Good filtrations for reductive groups 35
3.3 Canonical filtration 38
3.4 Good filtrations for semisimple groups 40
3.5 Good filtrations for semisimple, simply
connected groups 46
3.6 The canonical filtration revisited 49
3.7 A useful lemma 50
Chapter 4. The classical groups 52
4.1 Exterior powers 5 2
4.2 Miniscule weights 53
4.3 Exceptional weights 53
4.4 The first fundamental dominant weight 54
4.5 Some module homomorphisms 56
4.6 Character formulas 57
4.7 The canonical filtration again 59
4.8 The restriction of Y(X ) to Po 60
4.9 The restriction of Y(X ) to the maximal
parabolic subgroups r 70
Chapter 5. Homological algebra revisited 76
Chapter 6. G2 86
Chapter 7. F4 89
7.1 Introduction 89
7.2 Y(\x) 89
7.3 Y(A4) 92
7.4 Odd characteristic 98
7.5 Exact sequences 9 9
7.6 The restriction of Y(X,) to P 101
7.7 M, N/E and Y/S 109
7.8 Z = A\{a3J 110
7.9 Z = A\{a2 112
7.10 Z = A\{a1 117
7.11 Z arbitrary 124
7.12 Y(X2) ® Y(X2) 124
7.13 H^G) and H2(G) are true !28
Chapter 8. Eg 133
Chapter 9. E? 140
9.1 YU^ 140
9.2 Y(XC) 142
b
9.3 p * 2 or 7 143
9.4 The restriction of Y(X^) to Po l47
p / W
9.5 R1IndnE(D) 155
9.6 Character formulas I57
Vy _
9.7 R Inds E l60
9.8 Y(X7) 168
Chapter 10. Eg 169
10.1 YU^ 169
10.2 p * 2 or 7 173
10.3 The restriction of YCX .) to Po 178
P
10.4 R^niL^D) 185
10.5 Orbits and characters 187
p
10.6 I^Ind^tE) 194
i py
10.7 R IniL^F) 212
10.8 The case p = 7 224
Chapter 11. An example and applications 227
11.1 An example 227
11.2 Cohomology 228
11.3 Homomorphisms between Weyl modules 229
11.4 Canonical products 229
11.5 Filtrations overs 230
Chapter 12. Miscellany 234
12.1 Injective modules for parabolic subgroups 234
12.2 Kerapf's Vanishing Theorem for rank one groups 239
12.3 The Vanishing Theorem in characteristic 0 242
12.4 Induced modules and affine quotients 247
References 250
Index 254 |
| any_adam_object | 1 |
| author | Donkin, Stephen 1953- |
| author_GND | (DE-588)1210724472 |
| author_facet | Donkin, Stephen 1953- |
| author_role | aut |
| author_sort | Donkin, Stephen 1953- |
| author_variant | s d sd |
| building | Verbundindex |
| bvnumber | BV000466517 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 185f MAT 202f MAT 143f |
| ctrlnum | (OCoLC)230828346 (DE-599)BVBBV000466517 |
| dewey-full | 512/.22 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.22 510 |
| dewey-search | 512/.22 510 |
| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000466517 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-19T13:04:21Z |
| institution | BVB |
| isbn | 3540156682 0387156682 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000287466 |
| oclc_num | 230828346 |
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| physical | VII, 253 Seiten |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Donkin, Stephen 1953- (DE-588)1210724472 aut Rational representations of algebraic groups tensor products and filtrations Stephen Donkin Berlin, [u.a.] Springer [1985] © 1985 VII, 253 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1140 Algebraïsche groepen gtt Groupes linéaires algébriques Représentations de groupes Linear algebraic groups Representations of groups Darstellung (DE-588)4200624-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Filtration (DE-588)4017164-4 gnd rswk-swf Tensorprodukt (DE-588)4059478-6 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Darstellung (DE-588)4200624-7 s Tensorprodukt (DE-588)4059478-6 s Filtration (DE-588)4017164-4 s Erscheint auch als Online-Ausgabe 3-540-39589-X Lecture notes in mathematics 1140 (DE-604)BV000676446 1140 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000287466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Donkin, Stephen 1953- Rational representations of algebraic groups tensor products and filtrations Lecture notes in mathematics Algebraïsche groepen gtt Groupes linéaires algébriques Représentations de groupes Linear algebraic groups Representations of groups Darstellung (DE-588)4200624-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Filtration (DE-588)4017164-4 gnd Tensorprodukt (DE-588)4059478-6 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4200624-7 (DE-588)4148816-7 (DE-588)4017164-4 (DE-588)4059478-6 (DE-588)4001164-1 |
| title | Rational representations of algebraic groups tensor products and filtrations |
| title_auth | Rational representations of algebraic groups tensor products and filtrations |
| title_exact_search | Rational representations of algebraic groups tensor products and filtrations |
| title_full | Rational representations of algebraic groups tensor products and filtrations Stephen Donkin |
| title_fullStr | Rational representations of algebraic groups tensor products and filtrations Stephen Donkin |
| title_full_unstemmed | Rational representations of algebraic groups tensor products and filtrations Stephen Donkin |
| title_short | Rational representations of algebraic groups |
| title_sort | rational representations of algebraic groups tensor products and filtrations |
| title_sub | tensor products and filtrations |
| topic | Algebraïsche groepen gtt Groupes linéaires algébriques Représentations de groupes Linear algebraic groups Representations of groups Darstellung (DE-588)4200624-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Filtration (DE-588)4017164-4 gnd Tensorprodukt (DE-588)4059478-6 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Algebraïsche groepen Groupes linéaires algébriques Représentations de groupes Linear algebraic groups Representations of groups Darstellung Darstellungstheorie Filtration Tensorprodukt Algebraische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000287466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT donkinstephen rationalrepresentationsofalgebraicgroupstensorproductsandfiltrations |