Representations of shifted Yangians and finite W-algebras:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2008
|
| Series: | Memoirs of the American Mathematical Society
918 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 196, number 918 (end of volume )." Includes bibliographical references |
| Physical Description: | VII, 107 S. |
| ISBN: | 9780821842164 |
Staff View
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| 245 | 1 | 0 | |a Representations of shifted Yangians and finite W-algebras |c Jonathan Brundan ; Alexander Kleshchev |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 300 | |a VII, 107 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 918 | |
| 500 | |a "Volume 196, number 918 (end of volume )." | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Representations of quantum groups | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
Acknowledgements 8
Chapter 2. Shifted Yangians 9
2.1. Generators and relations 9
2.2. PBW theorem 10
2.3. Some automorphisms 12
2.4. Parabolic generators 13
2.5. Hopf algebra structure 18
2.6. The center of Yn(a) 20
Chapter 3. Finite W-algebras 23
3.1. Pyramids 23
3.2. Finite W-algebras 24
3.3. Invariants 25
3.4. Finite W-algebras are quotients of shifted Yangians 26
3.5. More automorphisms 27
3.6. Miura transform 28
3.7. Vanishing of higher T$ s 30
3.8. Harish-Chandra homomorphisms 32
Chapter 4. Dual canonical bases 35
4.1. Tableaux 35
4.2. Dual canonical bases 37
4.3. Crystals 40
4.4. Consequences of the Kazhdan-Lusztig conjecture 41
Chapter 5. Highest weight theory 47
5.1. Admissible modules 47
5.2. Gelfand-Tsetlin characters 47
5.3. Highest weight modules 49
5.4. Classification of admissible irreducible representations 50
5.5. Composition multiplicities 51
Chapter 6. Verma modules 53
6.1. Parametrization of highest weights 53
6.2. Characters of Verma modules 55
6.3. The linkage principle 57
6.4. The center of W(n) 59
6.5. Proof of Theorem 6.2 61
V
vi CONTENTS
Chapter 7. Standard modules 67
7.1. Two rows 67
7.2. Classification of finite dimensional irreducible representations 71
7.3. Tensor products 72
7.4. Characters of standard modules 77
7.5. Grothendieck groups 78
Chapter 8. Character formulae 81
8.1. Skryabin s theorem 81
8.2. Tensor identities 82
8.3. Translation functors 85
8.4. Translation commutes with duality 89
8.5. Whittaker functor 95
Notation 103
Bibliography 105
|
| adam_txt |
Contents
Chapter 1. Introduction 1
Acknowledgements 8
Chapter 2. Shifted Yangians 9
2.1. Generators and relations 9
2.2. PBW theorem 10
2.3. Some automorphisms 12
2.4. Parabolic generators 13
2.5. Hopf algebra structure 18
2.6. The center of Yn(a) 20
Chapter 3. Finite W-algebras 23
3.1. Pyramids 23
3.2. Finite W-algebras 24
3.3. Invariants 25
3.4. Finite W-algebras are quotients of shifted Yangians 26
3.5. More automorphisms 27
3.6. Miura transform 28
3.7. Vanishing of higher T$'s 30
3.8. Harish-Chandra homomorphisms 32
Chapter 4. Dual canonical bases 35
4.1. Tableaux 35
4.2. Dual canonical bases 37
4.3. Crystals 40
4.4. Consequences of the Kazhdan-Lusztig conjecture 41
Chapter 5. Highest weight theory 47
5.1. Admissible modules 47
5.2. Gelfand-Tsetlin characters 47
5.3. Highest weight modules 49
5.4. Classification of admissible irreducible representations 50
5.5. Composition multiplicities 51
Chapter 6. Verma modules 53
6.1. Parametrization of highest weights 53
6.2. Characters of Verma modules 55
6.3. The linkage principle 57
6.4. The center of W(n) 59
6.5. Proof of Theorem 6.2 61
V
vi CONTENTS
Chapter 7. Standard modules 67
7.1. Two rows 67
7.2. Classification of finite dimensional irreducible representations 71
7.3. Tensor products 72
7.4. Characters of standard modules 77
7.5. Grothendieck groups 78
Chapter 8. Character formulae 81
8.1. Skryabin's theorem 81
8.2. Tensor identities 82
8.3. Translation functors 85
8.4. Translation commutes with duality 89
8.5. Whittaker functor 95
Notation 103
Bibliography 105 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:53:12Z |
| indexdate | 2024-07-09T21:26:32Z |
| institution | BVB |
| isbn | 9780821842164 |
| language | English |
| lccn | 2008030300 |
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| physical | VII, 107 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Brundan, Jonathan Verfasser aut Representations of shifted Yangians and finite W-algebras Jonathan Brundan ; Alexander Kleshchev Providence, R.I. American Mathematical Society 2008 VII, 107 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 918 "Volume 196, number 918 (end of volume )." Includes bibliographical references Representations of quantum groups Lie superalgebras Lie-Superalgebra (DE-588)4304027-5 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Superalgebra (DE-588)4304027-5 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Kleščev, Aleksandr S. 1966- Verfasser (DE-588)136718264 aut Memoirs of the American Mathematical Society 918 (DE-604)BV008000141 918 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016974914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brundan, Jonathan Kleščev, Aleksandr S. 1966- Representations of shifted Yangians and finite W-algebras Memoirs of the American Mathematical Society Representations of quantum groups Lie superalgebras Lie-Superalgebra (DE-588)4304027-5 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4304027-5 (DE-588)4148816-7 |
| title | Representations of shifted Yangians and finite W-algebras |
| title_auth | Representations of shifted Yangians and finite W-algebras |
| title_exact_search | Representations of shifted Yangians and finite W-algebras |
| title_exact_search_txtP | Representations of shifted Yangians and finite W-algebras |
| title_full | Representations of shifted Yangians and finite W-algebras Jonathan Brundan ; Alexander Kleshchev |
| title_fullStr | Representations of shifted Yangians and finite W-algebras Jonathan Brundan ; Alexander Kleshchev |
| title_full_unstemmed | Representations of shifted Yangians and finite W-algebras Jonathan Brundan ; Alexander Kleshchev |
| title_short | Representations of shifted Yangians and finite W-algebras |
| title_sort | representations of shifted yangians and finite w algebras |
| topic | Representations of quantum groups Lie superalgebras Lie-Superalgebra (DE-588)4304027-5 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Representations of quantum groups Lie superalgebras Lie-Superalgebra Darstellungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016974914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT brundanjonathan representationsofshiftedyangiansandfinitewalgebras AT klescevaleksandrs representationsofshiftedyangiansandfinitewalgebras |