Quantum linear groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
1991
|
| Series: | Memoirs of the American Mathematical Society
439 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 89, Number 439 (second of 3 numbers) |
| Physical Description: | VI, 157 S. |
| ISBN: | 0821825011 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quantum linear groups |c Brian Parshall ; Jian-pan Wang |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1991 | |
| 300 | |a VI, 157 S. | ||
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Record in the Search Index
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| adam_text | Contents
Introduction 1
1. Quantum Groups 6
1.1. Quantum affine spaces 6
1.2. Quantum groups 6
1.3. Direct products 9
1 4. Closed subgroups 9
1.5. Normal closed subgroups 10
1.6. Kernels and exact sequences 11
1.7. Cartesian squares 12
1.8. Coverings 13
2. Representation Theory of Quantum Groups 15
2.1. Rational representations 15
2.2. Functorial description 15
2.3. Denning matrices 17
2.4. Contragradient modules and tensor products 17
2.5. Characters and character groups 21
2.6. Fixed points 22
2.7. Induction 22
2.8. Injective objects 24
2.9. Exact subgroups of quantum groups 26
2.10. A theorem on central faithfully flat morphisms 27
2.11. The Hochschild Serre spectral sequence 30
3. Quantum Matrix Spaces 32
3.1. Quadratic algebras 32
3.2. Quasi Yang Baxter algebras 32
3.3. Basis theorem for quasi Yang Baxter algebras 34
3.4. The quadratic algebras K[A^°] and K[A°J ] 36
3.5. The quantum matrix space Mq(n) 37
3.6. The bialgebra structure on K[Mq(n)] 39
iii
iv CONTENTS
3.7. Some automorphisms and anti automorphisms 40
3.8. K[Aql°] and K[A^n] as A [M,(n)] comodules 41
4. Quantum Determinants 42
4.1. Quantum determinant 42
4.2. First properties of the determinant 44
4.3. Subdeterminants 44
4.4. Laplace expansions 45
4.5. Some commutators, I 47
4.6. The centrality of the determinant 49
5. The Antipode and Quantum Linear Groups 51
5.1. Some commutators, II 51
5.2. Some commutators, III 54
5.3. Quantum general and special linear groups 56
5.4. A property of the antipode 58
6. Some Closed Subgroups 61
6.1. Parabolic and Levi subgroups 61
6.2. Some properties of the parabolic and Levi subgroups 64
6.3. Some remarks 67
6.4. Coadjoint action of the maximal torus and the root system 69
6.5. Character groups of Tq and Bq 71
7. Frobenius Morphisms and Kernels 72
7.1. Gaussian polynomials 72
7.2. Frobenius morphisms 75
7.3. Infinitesimal subgroups 78
7.4. Some homological properties of GLq(n) 79
7.5. Some exact subgroups of GLq(n) 79
8. Global Representation Theory 82
8.1. Density of the big cell 82
8.2. Highest weight modules 83
8.3. Some properties of induced Gg modules • 85
8.4. Induction to parabolic subgroups 86
8.5. The semisimple rank 1 case, I 92
8.6. The semisimple rank 1 case, II 94
8.7. The one to one correspondence between irreducible modules and dominant
weights 95
8.8. Formal characters and their invariance under the Weyl group 97
8.9. Injective modules for Borel subgroups 99
8.10. A finiteness theorem; Weyl modules 100
9. Infinitesimal Representation Theory 102
9.1. An infinitesimal version of the density theorem 102
9.2. Highest weight and irreducible representations for (G,)i T and (Gq)i B ¦¦¦ 103
9.3. Irreducible representations of (G,)i 104
9.4. The tensor product theorem 107
9.5. Induction to infinitesimal Borel subgroups 109
9.6. Induction from infinitesimal Borel subgroups ,1 110
CONTENTS v
9.7. Induction from infinitesimal Borel subgroups , II 114
9.8. Highest weight categories 116
9.9. Injective modules for (G,)i 119
9.10. The Steinberg module 120
10. The Generalization of Certain Important Theorems on the Cohomology
of Vector Bundles on the Flag Manifold 122
10.1. An isomorphism theorem and its consequences 122
10.2. Borel Weil Bott theorem for small dominant weights 125
10.3. Serre duality and strong linkage principle 128
10.4. Kempf vanishing theorem, good nitrations and Weyl character formula 131
10.5. A coalgebra isomorphism between K[GLq(n)] and K[GL q(n)] 133
11. g Schur Algebras 139
11.1. Polynomial representations of Gq 139
11.2. The g Schur algebraSq(n,r) 141
11.3. Sq(n,r) as an endomorphism algebra 142
11.4. On the complete reducibility of G, modules 145
11.5. Sq(n,r) as a quasi hereditary algebra 147
11.6. The generalization of a theorem of J. A. Green 151
11.7. Tensor product theorem for g Schur algebras 151
References 155
|
| any_adam_object | 1 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:11:56Z |
| institution | BVB |
| isbn | 0821825011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002707514 |
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| physical | VI, 157 S. |
| publishDate | 1991 |
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| spelling | Parshall, Brian 1945- Verfasser (DE-588)172302021 aut Quantum linear groups Brian Parshall ; Jian-pan Wang Providence, R.I. American Mathematical Society 1991 VI, 157 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 439 Volume 89, Number 439 (second of 3 numbers) Teoria Dos Grupos larpcal Group schemes (Mathematics) Linear algebraic groups Representations of groups Gruppenschema (DE-588)4022399-1 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf Lineare Gruppe (DE-588)4138778-8 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s DE-604 Darstellungstheorie (DE-588)4148816-7 s Lineare Gruppe (DE-588)4138778-8 s Gruppenschema (DE-588)4022399-1 s Wang, Jian-Pan Verfasser aut American Mathematical Society Memoirs of the American Mathematical Society 439 (DE-604)BV008000141 439 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002707514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parshall, Brian 1945- Wang, Jian-Pan Quantum linear groups Teoria Dos Grupos larpcal Group schemes (Mathematics) Linear algebraic groups Representations of groups Gruppenschema (DE-588)4022399-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd Quantengruppe (DE-588)4252437-4 gnd Lineare Gruppe (DE-588)4138778-8 gnd |
| subject_GND | (DE-588)4022399-1 (DE-588)4148816-7 (DE-588)4252437-4 (DE-588)4138778-8 |
| title | Quantum linear groups |
| title_auth | Quantum linear groups |
| title_exact_search | Quantum linear groups |
| title_full | Quantum linear groups Brian Parshall ; Jian-pan Wang |
| title_fullStr | Quantum linear groups Brian Parshall ; Jian-pan Wang |
| title_full_unstemmed | Quantum linear groups Brian Parshall ; Jian-pan Wang |
| title_short | Quantum linear groups |
| title_sort | quantum linear groups |
| topic | Teoria Dos Grupos larpcal Group schemes (Mathematics) Linear algebraic groups Representations of groups Gruppenschema (DE-588)4022399-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd Quantengruppe (DE-588)4252437-4 gnd Lineare Gruppe (DE-588)4138778-8 gnd |
| topic_facet | Teoria Dos Grupos Group schemes (Mathematics) Linear algebraic groups Representations of groups Gruppenschema Darstellungstheorie Quantengruppe Lineare Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002707514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT parshallbrian quantumlineargroups AT wangjianpan quantumlineargroups |