Representations of quantum algebras and combinatorics of Young tableaux:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Schriftenreihe: | University lecture series
Volume 26 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 158 Seiten Diagramme |
| ISBN: | 0821832328 9780821832325 |
Internformat
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| 240 | 1 | 0 | |a A(1) r−1-gata keiryoshigun no hyogenron to kumiawaseron |
| 245 | 1 | 0 | |a Representations of quantum algebras and combinatorics of Young tableaux |c Susumu Ariki. Translated from the Japanese and revised by the author |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
| 264 | 4 | |c © 2002 | |
| 300 | |a vii, 158 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Bases (Linear topological spaces) | |
| 650 | 4 | |a Representations of quantum groups | |
| 650 | 4 | |a Young tableaux | |
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| 650 | 0 | 7 | |a Darstellungstheorie |0 (DE-588)4148816-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804129303135256576 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1. Introduction 1
1.1. How do you do ? 1
1.2. What are we interested in ? 1
1.3. Enveloping algebras 3
Chapter 2. The Serre relations 9
2.1. The Serre relations 9
2.2. The quantum algebra of type Ar~i 13
Chapter 3. Kac Moody Lie algebras 15
3.1. Lie algebras by generators and relations 15
3.2. Kac Moody Lie algebras 17
3.3. The quantum algebra of type A^ 21
Chapter 4. Crystal bases of {/,, modules 23
4.1. Integrable modules 23
4.2. The Kashiwara operators 24
4.3. Crystal bases 27
Chapter 5. The tensor product of crystals 29
5.1. Basics of crystal bases 29
5.2. Tensor products of crystal bases 34
Chapter 6. Crystal bases of U~ 37
6.1. Triangular decomposition of Uv 37
6.2. Integrable highest weight modules 39
6.3. Crystal bases of U~ 42
Chapter 7. The canonical basis 47
7.1. A review of Lusztig s canonical basis 47
7.2. The lattice of the canonical basis 51
Chapter 8. Existence and uniqueness (part I) 55
8.1. Preparatory lemmas 55
8.2. The first main theorem 59
Chapter 9. Existence and uniqueness (part II) 61
9.1. Preparatory results 61
9.2. The second main theorem 65
V
vi CONTENTS
Chapter 10. The Hayashi realization 75
10.1. Partitions and the Hayashi realization 75
10.2. Generalization to the case of multipartitions 85
Chapter 11. Description of the crystal graph of ^(A) 87
11.1. A theorem for proving the Misra Miwa theorem 87
11.2. The Misra Miwa theorem 94
Chapter 12. An overview of the applications to Hecke algebras 97
12.1. The Hecke algebra of type G(m, 1, n) 97
12.2. Consequences of Theorem 12.5 101
Chapter 13. The Hecke algebra of type G(m, l,n) 105
13.1. The affine Hecke algebra 105
13.2. Semi normal representations 107
13.3. The decomposition map 111
13.4. Specht module theory 113
13.5. A theorem of Morita type 117
13.6. Refined induction and restriction functors 118
Chapter 14. The proof of Theorem 12.5 123
14.1. Representations of a cyclic quiver 123
14.2. The Hall algebra and the quantum algebra 127
14.3. Some results from the geometric theory 133
14.4. Proof of the generalized LLT conjecture 142
Chapter 15. Reference guide 147
Bibliography 149
Index 157
|
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| author | Ariki, Susumu 1959- |
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| discipline | Physik Mathematik |
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| id | DE-604.BV014471793 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:02:59Z |
| institution | BVB |
| isbn | 0821832328 9780821832325 |
| language | English Japanese |
| lccn | 2002025869 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009878396 |
| oclc_num | 49558690 |
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| physical | vii, 158 Seiten Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
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| series | University lecture series |
| series2 | University lecture series |
| spelling | Ariki, Susumu 1959- Verfasser (DE-588)102407210X aut A(1) r−1-gata keiryoshigun no hyogenron to kumiawaseron Representations of quantum algebras and combinatorics of Young tableaux Susumu Ariki. Translated from the Japanese and revised by the author Providence, Rhode Island American Mathematical Society [2002] © 2002 vii, 158 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 26 Algebraïsche topologie gtt Kwantumgroepen gtt Representatie (algemeen) gtt Bases (Linear topological spaces) Representations of quantum groups Young tableaux Youngsches Tableau (DE-588)4190432-1 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s Darstellungstheorie (DE-588)4148816-7 s Youngsches Tableau (DE-588)4190432-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1833-5 University lecture series Volume 26 (DE-604)BV004153846 26 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878396&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ariki, Susumu 1959- Representations of quantum algebras and combinatorics of Young tableaux University lecture series Algebraïsche topologie gtt Kwantumgroepen gtt Representatie (algemeen) gtt Bases (Linear topological spaces) Representations of quantum groups Young tableaux Youngsches Tableau (DE-588)4190432-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4190432-1 (DE-588)4148816-7 (DE-588)4252437-4 |
| title | Representations of quantum algebras and combinatorics of Young tableaux |
| title_alt | A(1) r−1-gata keiryoshigun no hyogenron to kumiawaseron |
| title_auth | Representations of quantum algebras and combinatorics of Young tableaux |
| title_exact_search | Representations of quantum algebras and combinatorics of Young tableaux |
| title_full | Representations of quantum algebras and combinatorics of Young tableaux Susumu Ariki. Translated from the Japanese and revised by the author |
| title_fullStr | Representations of quantum algebras and combinatorics of Young tableaux Susumu Ariki. Translated from the Japanese and revised by the author |
| title_full_unstemmed | Representations of quantum algebras and combinatorics of Young tableaux Susumu Ariki. Translated from the Japanese and revised by the author |
| title_short | Representations of quantum algebras and combinatorics of Young tableaux |
| title_sort | representations of quantum algebras and combinatorics of young tableaux |
| topic | Algebraïsche topologie gtt Kwantumgroepen gtt Representatie (algemeen) gtt Bases (Linear topological spaces) Representations of quantum groups Young tableaux Youngsches Tableau (DE-588)4190432-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Algebraïsche topologie Kwantumgroepen Representatie (algemeen) Bases (Linear topological spaces) Representations of quantum groups Young tableaux Youngsches Tableau Darstellungstheorie Quantengruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878396&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
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