Polynomial representations of GLn:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1980
|
| Series: | Lecture notes in mathematics
830 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 118 S. |
| ISBN: | 3540102582 0387102582 |
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MARC
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Record in the Search Index
| _version_ | 1804116722216599552 |
|---|---|
| adam_text | POLYNOMIAL REPRESENTATIONS OF GL
n
Table of Contents
Chapter 1. Introduction 1
Chapter 2. Polynomial representations of GL (K) :
n
The Schur algebra 18
2.1 Notation, etc. 18
2.2 The categories M^n) .M^n.r) 19
2.3 The Schur algebra SK(n,r) 21
2.4 The map e:KF S (n,r) 23
K
2.5 Modular theory 25
2.6 The module EBr 27
2.7 Contravariant duality 31
2.8 A^n.r) as Kr bimodule 34
Chapter 3. Weights and characters 36
3.1 Weights 36
3.2 Weight spaces 37
3.3 Some properties of weight spaces 38
3.4 Characters 40
3.5 Irreducible modules in M^(n,r) 44
Chapter 4. The modules D 50
A, K
4.1 Preamble 50
4.2 A tableaux 50
4.3 Bideterminants 51
4.4 Definition of D. „ 53
VI
4.5 The basis theorem for D, 55
A ,K
4.6 The Carter Lusztig lemma 57
4.7 Some consequences of the basis theorem 59
4.8 James s construction of D 61
A j Jx
Chapter 5. The Carter Lusztig modules V 65
A j Is.
5.1 Definition of V. „ 65
A ,K
5.2 V is Carter Lusztig s Weyl module 65
A j K
5.3 The Carter Lusztig basis for V 68
A., K.
5.4 Some consequences of the basis theorem 70
5.5 Contravariant forms on V 73
A ,K
5.6 Z forms of V 77
A ,CJ
Chapter 6. Representation theory of the symmetric
group 80
6.1 The functor fiM^n.r) + mod KG(r)(r S n) 80
6.2 General theory of the functor
f :mod S ¦ mod eSe 83
6.3 Application I. Specht modules
and their duals 88
6.4 Application II. Irreducible
KG(r) modules, char K = p 93
6.5 Application III. The functor
MjjCN.r) • M^n.r) (N _ n) 102
6.6 Application IV. Some theorems on
decomposition numbers 107
Bibliography 113
Index 117
|
| any_adam_object | 1 |
| author | Green, James Alexander |
| author_facet | Green, James Alexander |
| author_role | aut |
| author_sort | Green, James Alexander |
| author_variant | j a g ja jag |
| building | Verbundindex |
| bvnumber | BV002264593 |
| 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 SK 260 |
| ctrlnum | (OCoLC)6816086 (DE-599)BVBBV002264593 |
| dewey-full | 510 512/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.5 |
| dewey-search | 510 512/.5 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Polynomdarstellung gnd |
| genre_facet | Polynomdarstellung |
| id | DE-604.BV002264593 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:01Z |
| institution | BVB |
| isbn | 3540102582 0387102582 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488175 |
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| physical | VI, 118 S. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Green, James Alexander Verfasser aut Polynomial representations of GLn J. A. Green Berlin [u.a.] Springer 1980 VI, 118 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 830 Groupes linéaires algébriques Groupes symétriques Lineaire groepen gtt Polynomen gtt Représentations de groupes Symmetriegroepen gtt Linear algebraic groups Representations of groups Symmetry groups Lineare Gruppe (DE-588)4138778-8 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Allgemeine lineare Gruppe (DE-588)4284587-7 gnd rswk-swf Darstellung (DE-588)4200624-7 gnd rswk-swf Schur-Algebra (DE-588)4180242-1 gnd rswk-swf Polynomdarstellung gnd rswk-swf Lineare Gruppe (DE-588)4138778-8 s Polynomdarstellung f DE-604 Schur-Algebra (DE-588)4180242-1 s Polynom (DE-588)4046711-9 s Darstellung (DE-588)4200624-7 s 1\p DE-604 Allgemeine lineare Gruppe (DE-588)4284587-7 s Darstellung Mathematik (DE-588)4128289-9 s 2\p DE-604 Lecture notes in mathematics 830 (DE-604)BV000676446 830 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Green, James Alexander Polynomial representations of GLn Lecture notes in mathematics Groupes linéaires algébriques Groupes symétriques Lineaire groepen gtt Polynomen gtt Représentations de groupes Symmetriegroepen gtt Linear algebraic groups Representations of groups Symmetry groups Lineare Gruppe (DE-588)4138778-8 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Polynom (DE-588)4046711-9 gnd Allgemeine lineare Gruppe (DE-588)4284587-7 gnd Darstellung (DE-588)4200624-7 gnd Schur-Algebra (DE-588)4180242-1 gnd |
| subject_GND | (DE-588)4138778-8 (DE-588)4128289-9 (DE-588)4046711-9 (DE-588)4284587-7 (DE-588)4200624-7 (DE-588)4180242-1 |
| title | Polynomial representations of GLn |
| title_auth | Polynomial representations of GLn |
| title_exact_search | Polynomial representations of GLn |
| title_full | Polynomial representations of GLn J. A. Green |
| title_fullStr | Polynomial representations of GLn J. A. Green |
| title_full_unstemmed | Polynomial representations of GLn J. A. Green |
| title_short | Polynomial representations of GLn |
| title_sort | polynomial representations of gln |
| topic | Groupes linéaires algébriques Groupes symétriques Lineaire groepen gtt Polynomen gtt Représentations de groupes Symmetriegroepen gtt Linear algebraic groups Representations of groups Symmetry groups Lineare Gruppe (DE-588)4138778-8 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Polynom (DE-588)4046711-9 gnd Allgemeine lineare Gruppe (DE-588)4284587-7 gnd Darstellung (DE-588)4200624-7 gnd Schur-Algebra (DE-588)4180242-1 gnd |
| topic_facet | Groupes linéaires algébriques Groupes symétriques Lineaire groepen Polynomen Représentations de groupes Symmetriegroepen Linear algebraic groups Representations of groups Symmetry groups Lineare Gruppe Darstellung Mathematik Polynom Allgemeine lineare Gruppe Darstellung Schur-Algebra Polynomdarstellung |
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