Factorizable sheaves and quantum groups:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Lecture notes in mathematics
1691 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 287 S. |
| ISBN: | 3540646191 |
Internformat
MARC
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| 100 | 1 | |a Bezrukavnikov, Roman |d 1973- |e Verfasser |0 (DE-588)120389118 |4 aut | |
| 245 | 1 | 0 | |a Factorizable sheaves and quantum groups |c Roman Bezrukavnikov ; Michael Finkelberg ; Vadim Schechtman |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a X, 287 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1691 | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Quantum groups | |
| 650 | 4 | |a Representations of groups | |
| 650 | 4 | |a Sheaf theory | |
| 650 | 0 | 7 | |a Quantengruppe |0 (DE-588)4252437-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Garbe |g Mathematik |0 (DE-588)4019261-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Finkelʹberg, Michail |d 1967- |e Verfasser |0 (DE-588)120389169 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008125219 | ||
Datensatz im Suchindex
| _version_ | 1804126602690297856 |
|---|---|
| adam_text | Table of contents
Introduction 1
Acknowledgement 5
Part 0. OVERVIEW
1. Introduction 6
Chapter 1. Local
2. The category C 11
3. Braiding local systems 15
4. Factorizable sheaves 19
5. Tensor product 20
6. Vanishing cycles 23
Chapter 2. Global (genus 0)
7. Cohesive local systems 27
8. Gluing 30
9. Semiinfinite cohomology 31
10. Conformal blocks (genus 0) 33
11. Integration 35
12. Regular representation 36
13. Regular sheaf 37
Chapter 3. Modular
14. Heisenberg local system 40
15. Fusion structures on FS 46
16. Conformal blocks (higher genus) 48
VII
Part I. INTERSECTION COHOMOLOGY
OF REAL ARRANGEMENTS
1. Introduction 50
2. Topological preliminaries 51
3. Vanishing cycles functors 55
4. Computations for standard sheaves 63
Part II. CONFIGURATION SPACES AND QUANTUM GROUPS
1. Introduction 71
Chapter 1. Algebraic discussion
2. Free algebras and bilinear forms 73
3. Hochschild complexes 82
4. Symmetrization 84
5. Quotient algebras 87
Chapter 2. Geometric discussion
6. Diagonal stratification and related algebras 89
7. Principal stratification 94
8. Standard sheaves 100
Chapter 3. Fusion
9. Additivity theorem 110
10. Fusion and tensor products 112
Chapter 4. Category C
11. Simply laced case 116
12. Non simply laced case 119
VIII
Part III. TENSOR CATEGORIES ARISING FROM
CONFIGURATION SPACES
1. Introduction 122
Chapter 1. Category !FS
2. Space A 124
3. Braiding local system 1 126
4. Factorizable sheaves 128
5. Finite sheaves 130
6. Standard sheaves 132
Chapter 2. Tensor structure
7. Marked disk operad 134
8. Cohesive local systems KI 138
9. Factorizable sheaves over K A 139
10. Gluing 142
11. Fusion 145
Chapter 3. Functor $
12. Functor $ 150
13. Main properties of $ 159
Chapter 4. Equivalence
14. Truncation functors 162
15. Rigidity 165
16. Steinberg sheaf 167
17. Equivalence 169
18. The case of generic C 170
Part IV. LOCALIZATION OVER P1
1. Introduction 173
IX
Chapter 1. Gluing over P1
2. Cohesive local system 174
3. Gluing 176
Chapter 2. Semiinifinite cohomology
4. Semiinfinite functors Ext and Tor in C 180
5. Some calculations 184
Chapter 3. Global sections
6. Braiding and balance in C and TS 188
7. Global sections over A(K) 189
8. Global sections over V 190
9. Application to conformal blocks 193
Part V. MODULAR STRUCTURE ON THE CATEGORY TS
1. Introduction 197
Chapter 1. Heisenberg local system
2. Notations and statement of the main result 199
3. The scheme of construction 202
4. The universal line bundle 204
5. The universal local system 207
6. Factorization isomorphisms 216
Chapter 2. The modular property of the Heisenberg system
7. Degeneration of curves: recollections and notations 219
8. Proof of Theorem 7.6(a) 221
9. Proof of Theorem 7.6(b) 224
Chapter 3. Regular representation
10. A characterization of the regular bimodule 231
11. The adjoint representation 233
X
Chapter 4. Quadratic degeneration in genus zero
12. / sheaves 235
13. Degenerations of quadrics 236
14. The / sheaf Tl 237
15. Convolution 239
Chapter 5. Modular functor
16. Gluing over C 242
17. Degeneration of factorizable sheaves 246
18. Global sections over C 248
Chapter 6. Integral representations of conformal blocks
19. Conformal blocks in arbitrary genus 249
References 252
Index of Notation 254
Index of Terminology 283
|
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| author | Bezrukavnikov, Roman 1973- Finkelʹberg, Michail 1967- Schechtman, Vadim 1954- |
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| id | DE-604.BV012006568 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:20:04Z |
| institution | BVB |
| isbn | 3540646191 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008125219 |
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| physical | X, 287 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bezrukavnikov, Roman 1973- Verfasser (DE-588)120389118 aut Factorizable sheaves and quantum groups Roman Bezrukavnikov ; Michael Finkelberg ; Vadim Schechtman Berlin [u.a.] Springer 1998 X, 287 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1691 Mathematische Physik Mathematical physics Quantum groups Representations of groups Sheaf theory Quantengruppe (DE-588)4252437-4 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s Garbe Mathematik (DE-588)4019261-1 s DE-604 Finkelʹberg, Michail 1967- Verfasser (DE-588)120389169 aut Schechtman, Vadim 1954- Verfasser (DE-588)120389193 aut Lecture notes in mathematics 1691 (DE-604)BV000676446 1691 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008125219&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bezrukavnikov, Roman 1973- Finkelʹberg, Michail 1967- Schechtman, Vadim 1954- Factorizable sheaves and quantum groups Lecture notes in mathematics Mathematische Physik Mathematical physics Quantum groups Representations of groups Sheaf theory Quantengruppe (DE-588)4252437-4 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| subject_GND | (DE-588)4252437-4 (DE-588)4019261-1 |
| title | Factorizable sheaves and quantum groups |
| title_auth | Factorizable sheaves and quantum groups |
| title_exact_search | Factorizable sheaves and quantum groups |
| title_full | Factorizable sheaves and quantum groups Roman Bezrukavnikov ; Michael Finkelberg ; Vadim Schechtman |
| title_fullStr | Factorizable sheaves and quantum groups Roman Bezrukavnikov ; Michael Finkelberg ; Vadim Schechtman |
| title_full_unstemmed | Factorizable sheaves and quantum groups Roman Bezrukavnikov ; Michael Finkelberg ; Vadim Schechtman |
| title_short | Factorizable sheaves and quantum groups |
| title_sort | factorizable sheaves and quantum groups |
| topic | Mathematische Physik Mathematical physics Quantum groups Representations of groups Sheaf theory Quantengruppe (DE-588)4252437-4 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| topic_facet | Mathematische Physik Mathematical physics Quantum groups Representations of groups Sheaf theory Quantengruppe Garbe Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008125219&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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