The symmetric group: representations, combinatorial algorithms, and symmetric functions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
[2001]
|
| Edition: | Second edition |
| Series: | Graduate texts in mathematics
203 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Aufl. bei Wadsworth, Inc. erschienen |
| Physical Description: | XV, 238 Seiten Diagramme |
| ISBN: | 0387950672 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the 2nd Edition v
Preface to the 1st Eition vii
1 Group Representations 1
1.1 Fundamental Concepts 1
1.2 Matrix Representations 4
1.3 G Modules and the Group Algebra 6
1.4 Reducibility 10
1.5 Complete Reducibility and Maschke s
Theorem 13
1.6 G Homomorphisms and Schur s Lemma 18
1.7 Commutant and Endomorphism Algebras 23
1.8 Group Characters 30
1.9 Inner Products of Characters 33
1.10 Decomposition of the Group Algebra 40
1.11 Tensor Products Again 43
1.12 Restricted and Induced Representations 45
1.13 Exercises 48
2 Representations of the Symmetric Group 53
2.1 Young Subgroups, Tableaux, and Tabloids 53
2.2 Dominance and Lexicographic Ordering 57
2.3 Specht Modules 60
2.4 The Submodule Theorem 63
2.5 Standard Tableaux and a Basis for Sx 66
2.6 Garnir Elements 70
2.7 Young s Natural Representation 74
2.8 The Branching Rule 76
2.9 The Decomposition of M 78
2.10 The Semistandard Basis for Hom(S M ) 82
2.11 Kostka Numbers and Young s Rule 85
2.12 Exercises 86
ix
x CONTENTS
3 Combinatorial Algorithms 91
3.1 The Robinson Schensted Algorithm 91
3.2 Column Insertion 95
3.3 Increasing and Decreasing Subsequences 97
3.4 The Knuth Relations 99
3.5 Subsequences Again 102
3.6 Viennot s Geometric Construction 106
3.7 Schiitzenberger s Jeu de Taquin 112
3.8 Dual Equivalence 116
3.9 Evacuation 121
3.10 The Hook Formula 124
3.11 The Determinantal Formula 132
3.12 Exercises 133
4 Symmetric Functions 141
4.1 Introduction to Generating Functions 142
4.2 The Hillman Grassl Algorithm 147
4.3 The Ring of Symmetric Functions 151
4.4 Schur Functions 155
4.5 The Jacobi Trudi Determinants 158
4.6 Other Definitions of the Schur Function 163
4.7 The Characteristic Map 167
4.8 Knuth s Algorithm 169
4.9 The Littlewood Richardson Rule 174
4.10 The Murnaghan Nakayama Rule 179
4.11 Exercises 185
5 Applications and Generalizations 191
5.1 Young s Lattice and Differential Posets 191
5.2 Growths and Local Rules 197
5.3 Groups Acting on Posets 204
5.4 Unimodality 208
5.5 Chromatic Symmetric Functions 213
5.6 Exercises 218
Bibliography 223
Index 230
|
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| dewey-search | 512.2 |
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| discipline | Mathematik |
| edition | Second edition |
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| id | DE-604.BV013731094 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:50:59Z |
| institution | BVB |
| isbn | 0387950672 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009384282 |
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| physical | XV, 238 Seiten Diagramme |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Sagan, Bruce E. 1954- Verfasser (DE-588)113115393 aut The symmetric group representations, combinatorial algorithms, and symmetric functions Bruce E. Sagan Second edition New York [u.a.] Springer [2001] XV, 238 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 203 1. Aufl. bei Wadsworth, Inc. erschienen Symmetrische Gruppe - Darstellung <Mathematik> Representations of groups Symmetric functions Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Symmetrische Gruppe (DE-588)4184204-2 s DE-604 Darstellung Mathematik (DE-588)4128289-9 s Erscheint auch als Online-Ausgabe 978-1-4757-6804-6 Graduate texts in mathematics 203 (DE-604)BV000000067 203 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009384282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sagan, Bruce E. 1954- The symmetric group representations, combinatorial algorithms, and symmetric functions Graduate texts in mathematics Symmetrische Gruppe - Darstellung <Mathematik> Representations of groups Symmetric functions Symmetrische Gruppe (DE-588)4184204-2 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| subject_GND | (DE-588)4184204-2 (DE-588)4128289-9 |
| title | The symmetric group representations, combinatorial algorithms, and symmetric functions |
| title_auth | The symmetric group representations, combinatorial algorithms, and symmetric functions |
| title_exact_search | The symmetric group representations, combinatorial algorithms, and symmetric functions |
| title_full | The symmetric group representations, combinatorial algorithms, and symmetric functions Bruce E. Sagan |
| title_fullStr | The symmetric group representations, combinatorial algorithms, and symmetric functions Bruce E. Sagan |
| title_full_unstemmed | The symmetric group representations, combinatorial algorithms, and symmetric functions Bruce E. Sagan |
| title_short | The symmetric group |
| title_sort | the symmetric group representations combinatorial algorithms and symmetric functions |
| title_sub | representations, combinatorial algorithms, and symmetric functions |
| topic | Symmetrische Gruppe - Darstellung <Mathematik> Representations of groups Symmetric functions Symmetrische Gruppe (DE-588)4184204-2 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| topic_facet | Symmetrische Gruppe - Darstellung <Mathematik> Representations of groups Symmetric functions Symmetrische Gruppe Darstellung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009384282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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