Introduction to quantum groups and crystal bases:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2002
|
| Schriftenreihe: | Graduate studies in mathematics
42 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 307 S. graph. Darst. |
| ISBN: | 0821828746 |
Internformat
MARC
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| 100 | 1 | |a Hong, Jin |d 1972- |e Verfasser |0 (DE-588)173537545 |4 aut | |
| 245 | 1 | 0 | |a Introduction to quantum groups and crystal bases |c Jin Hong ; Seok-Jin Kang |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2002 | |
| 300 | |a XVIII, 307 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 42 | |
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Datensatz im Suchindex
| _version_ | 1804129065818390528 |
|---|---|
| adam_text | Contents
Introduction xi
Chapter 1. Lie Algebras and Hopf Algebras 1
§1.1. Lie algebras 1
§1.2. Representations of Lie algebras 3
§1.3. The Lie algebra sl(2, F) 6
§1.4. The special linear Lie algebra sl(n, F) 8
§1.5. Hopf algebras 13
Exercises 19
Chapter 2. Kac Moody Algebras 21
§2.1. Kac Moody algebras 21
§2.2. Classification of generalized Cartan matrices 25
§2.3. Representation theory of Kac Moody algebras 27
§2.4. The category Oml 30
Exercises 34
Chapter 3. Quantum Groups 37
§3.1. Quantum groups 37
§3.2. Representation theory of quantum groups 43
§3.3. Ai forms 47
§3.4. Classical limit 51
§3.5. Complete reducibility of the category O?nt 57
Exercises 60
vii
Chapter 4. Crystal Bases 63
§4.1. Kashiwara operators 63
§4.2. Crystal bases and crystal graphs 66
§4.3. Crystal bases for Uq(5(2) modules 73
§4.4. Tensor product rule 77
§4.5. Crystals 85
Exercises 89
Chapter 5. Existence and Uniqueness of Crystal Bases 91
§5.1. Existence of crystal bases 91
§5.2. Uniqueness of crystal bases 97
§5.3. Kashiwara s grand loop argument 101
Exercises 116
Chapter 6. Global Bases 119
§6.1. Balanced triple 119
§6.2. Global basis for V(A) 122
§6.3. Polarization on U~ (g) 127
§6.4. Triviality of vector bundles over P1 132
§6.5. Existence of global bases 139
Exercises 147
Chapter 7. Young Tableaux and Crystals 149
§7.1. The quantum group Uq{gin) 149
§7.2. The category O|° 152
§7.3. Tableaux and crystals 155
§7.4. Crystal graphs for Uq(gin) mod i es 161
Exercises 167
Chapter 8. Crystal Graphs for Classical Lie Algebras 169
§8.1. Example: C/g(i?3) crystals 170
§8.2. Realization of Uq{An {] cvysta s 179
§8.3. Realization of [/g(Cn) crystals 181
§8.4. Realization of [/9(5n) crystals 190
§8.5. Realization of t/g(Z?n) crystals 197
§8.6. Tensor product decomposition of crystals 203
Exercises 207
Chapter 9. Solvable Lattice Models 209
§9.1. The 6 vertex model 209
§9.2. The quantum affine algebra Uq{s 2) 215
§9.3. Crystals and paths 222
Exercises 227
Chapter 10. Perfect Crystals 229
§10.1. Quantum afrme algebras 229
§10.2. Energy functions and combinatorial i? matrices 235
§10.3. Vertex operators for C/9(sl2) modules 239
§10.4. Vertex operators for quantum affine algebras 242
§10.5. Perfect crystals 247
§10.6. Path realization of crystal graphs 252
Exercises 260
Chapter 11. Combinatorics of Young Walls 263
§11.1. Perfect crystals of level 1 and path realization 263
§11.2. Combinatorics of Young walls 269
§11.3. The crystal structure 277
§11.4. Crystal graphs for basic representations 281
Exercises 295
Bibliography 297
Index of symbols 301
Index 305
|
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| bvnumber | BV014187004 |
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| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:13Z |
| institution | BVB |
| isbn | 0821828746 |
| language | English |
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| physical | XVIII, 307 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Hong, Jin 1972- Verfasser (DE-588)173537545 aut Introduction to quantum groups and crystal bases Jin Hong ; Seok-Jin Kang Providence, RI American Mathematical Society 2002 XVIII, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 42 Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Gruppentheorie (DE-588)4072157-7 s DE-188 Kang, Seok-Jin Verfasser aut Graduate studies in mathematics 42 (DE-604)BV009739289 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009724570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hong, Jin 1972- Kang, Seok-Jin Introduction to quantum groups and crystal bases Graduate studies in mathematics Darstellungstheorie (DE-588)4148816-7 gnd Gruppentheorie (DE-588)4072157-7 gnd Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4072157-7 (DE-588)4252437-4 |
| title | Introduction to quantum groups and crystal bases |
| title_auth | Introduction to quantum groups and crystal bases |
| title_exact_search | Introduction to quantum groups and crystal bases |
| title_full | Introduction to quantum groups and crystal bases Jin Hong ; Seok-Jin Kang |
| title_fullStr | Introduction to quantum groups and crystal bases Jin Hong ; Seok-Jin Kang |
| title_full_unstemmed | Introduction to quantum groups and crystal bases Jin Hong ; Seok-Jin Kang |
| title_short | Introduction to quantum groups and crystal bases |
| title_sort | introduction to quantum groups and crystal bases |
| topic | Darstellungstheorie (DE-588)4148816-7 gnd Gruppentheorie (DE-588)4072157-7 gnd Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Darstellungstheorie Gruppentheorie Quantengruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009724570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT hongjin introductiontoquantumgroupsandcrystalbases AT kangseokjin introductiontoquantumgroupsandcrystalbases |