Yangians and classical Lie algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2007]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xviii, 400 Seiten |
| ISBN: | 9780821843741 |
Internformat
MARC
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| 245 | 1 | 0 | |a Yangians and classical Lie algebras |c Alexander Molev |
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| 264 | 4 | |c © 2007 | |
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 143 | |
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Datensatz im Suchindex
| _version_ | 1804142676687192064 |
|---|---|
| adam_text | Contents
Preface xi
Chapter 1. Yangian for qIn 1
1.1. Defining relations 1
1.2. Matrix form of the defining relations 2
1.3. Automorphisms and anti-automorphisms 5
1.4. Poincare-Birkhoff-Witt theorem 7
1.5. Hopf algebra structure 9
1.6. Quantum determinant and quantum minors 12
1.7. Center of the algebra Yfj^) 16
1.8. Yangian for sljy 18
1.9. Quantum Liouville formula 20
1.10. Factorization of the quantum determinant 23
1.11. Gauss decomposition 27
1.12. Quantum Sylvester theorem 31
1.13. Gelfand-Tsetlin subalgebra 33
1.14. Bethe subalgebras 34
1.15. Examples 36
Bibliographical notes 42
Chapter 2. Twisted Yangians 45
2.1. Defining relations 45
2.2. Matrix form of the denning relations 47
2.3. Automorphisms and anti-automorphisms 48
2.4. Embedding into the Yangian 49
2.5. Sklyanin determinant 52
2.6. Sklyanin minors 56
2.7. Explicit formula for the Sklyanin determinant 59
2.8. The center of the twisted Yangian 64
2.9. The special twisted Yangian 66
2.10. Coideal property 67
2.11. Quantum Liouville formula 68
2.12. Factorization of the Sklyanin determinant 70
2.13. Extended twisted Yangian 72
2.14. Quantum Sylvester theorem 77
2.15. An equivalent presentation of Y(fljv) 82
2.16. Examples 85
Bibliographical notes 91
Chapter 3. Irreducible representations of Y(g[jy) 93
3.1. Drinfeld presentation of the Yangian 93
3.2. Highest weight representations 104
3.3. Representations of Y(gl2) HI
3.4. Representations of Y(fll^) 120
3.5. Examples 124
Bibliographical notes 128
Chapter 4. Irreducible representations of Y(qn) 131
4.1. Split presentation of the twisted Yangian 131
4.2. Highest weight representations 137
4.3. Representations of Y(sp2n) 145
4.4. Representations of Y(o2n) 154
4.5. Representations of Y(o2n+i) 168
4.6. Examples 182
Bibliographical notes 184
Chapter 5. Gelfand-Tsetlin bases for representations of Y(glN) 185
5.1. Yangian of level p 185
5.2. Lowering and raising operators 189
5.3. Action of the Drinfeld generators 195
5.4. Gelfand-Tsetlin bases for representations of giN 197
5.5. Examples 200
Bibliographical notes 201
Chapter 6. Tensor products of evaluation modules for Y(qIn) 203
6.1. Sufficient conditions 203
6.2. Necessary conditions 208
6.3. Irreducibility criterion 220
6.4. Fusion procedure for the symmetric group 223
6.5. Multiple tensor products 229
6.6. Examples 236
Bibliographical notes 237
Chapter 7. Casimir elements and Capelli identities 239
7.1. Newton s formulas 239
7.2. Noncommutative Cayley-Hamilton theorem 245
7.3. Graphical constructions of Casimir elements 246
7.4. Higher Capelli identities and quantum immanants 253
7.5. Noncommutative Pfaffians and Hafnians 262
7.6. Capelli identities for Ojv and sp2n 266
7.7. Examples 271
Bibliographical notes 275
Chapter 8. Centralizer construction 279
8.1. Olshanski algebra associated with gl^ 279
8.2. Virtual Casimir elements and highest weight modules for gl^ 281
8.3. Polynomial invariants for g^ 286
8.4. Algebraic structure of A^^) 291
8.5. Skew representations of Y(g[JV) 295
8.6. Olshanski algebra associated with g^ 300
8.7. Virtual Casimir elements and highest weight modules for floo 301
8.8. Polynomial invariants for gjv 304
8.9. Algebraic structure of A(goo) 311
8.10. Examples 316
Bibliographical notes 320
Chapter 9. Weight bases for representations of gjv 323
9.1. The Mickelsson algebra theory 323
9.2. Mickelsson-Zhelobenko algebra Z(B^r,g^_2) 326
9.3. Twisted Yangian and Mickelsson-Zhelobenko algebra 331
9.4. Yangian action on the multiplicity space 341
9.5. Basis of the multiplicity space 352
9.6. Basis of V(X) 356
9.7. Examples 375
Bibliographical notes 379
Bibliography 381
Index 399
|
| any_adam_object | 1 |
| author | Molev, Alexander 1961- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 |
| dewey-search | 512.482 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025508340 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:35:33Z |
| institution | BVB |
| isbn | 9780821843741 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020118807 |
| oclc_num | 255612379 |
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| owner | DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-19 DE-BY-UBM |
| physical | xviii, 400 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Molev, Alexander 1961- Verfasser (DE-588)1147020868 aut Yangians and classical Lie algebras Alexander Molev Providence, Rhode Island American Mathematical Society [2007] © 2007 xviii, 400 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 143 Quantengruppe (DE-588)4252437-4 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Quantengruppe (DE-588)4252437-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1370-5 Mathematical surveys and monographs Volume 143 (DE-604)BV000018014 143 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020118807&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Molev, Alexander 1961- Yangians and classical Lie algebras Mathematical surveys and monographs Quantengruppe (DE-588)4252437-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4252437-4 (DE-588)4130355-6 |
| title | Yangians and classical Lie algebras |
| title_auth | Yangians and classical Lie algebras |
| title_exact_search | Yangians and classical Lie algebras |
| title_full | Yangians and classical Lie algebras Alexander Molev |
| title_fullStr | Yangians and classical Lie algebras Alexander Molev |
| title_full_unstemmed | Yangians and classical Lie algebras Alexander Molev |
| title_short | Yangians and classical Lie algebras |
| title_sort | yangians and classical lie algebras |
| topic | Quantengruppe (DE-588)4252437-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Quantengruppe Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020118807&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT molevalexander yangiansandclassicalliealgebras |