Langlands correspondence for loop groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York ; Melbourne ; New Delhi ; Singapore
Cambridge University Press
2007
|
| Series: | Cambridge studies in advanced mathematics
103 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Physical Description: | xvi, 379 Seiten |
| ISBN: | 0521854431 9780521854436 |
Staff View
MARC
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| 100 | 1 | |a Frenkel, Edward |d 1968- |e Verfasser |0 (DE-588)173510116 |4 aut | |
| 245 | 1 | 0 | |a Langlands correspondence for loop groups |c Edward Frenkel |
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| 264 | 4 | |c © 2007 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
page
xi
1
Local
Langlands
correspondence
1
1.1
The classical theory
1
1.2 Langlands
parameters over the complex field
9
1.3
Representations of loop groups
18
2
Vertex algebras
31
2.1
The center
31
2.2
Basics of vertex algebras
38
2.3
Associativity in vertex algebras
52
3
Constructing central elements
61
3.1
Segal-Sugawara operators
62
3.2
Lie algebras associated to vertex algebras
70
3.3
The center of a vertex algebra
76
3.4
Jet schemes
81
3.5
The center in the case of sl2
87
4
Opers and the center for a general Lie algebra
101
4.1
Projective
connections, revisited
101
4.2
Opers for a general simple Lie algebra
107
4.3
The center for an arbitrary
affine
Кас
-Moody algebra
117
5
Free field realization
126
5.1
Overview
126
5.2
Finite-dimensional case
128
5.3
The case of
affine
algebras
135
5.4
Vertex algebra interpretation
140
5.5
Computation of the two-cocycle
145
5.6
Comparison of cohomology classes
151
6
Wakimoto modules
161
6.1
Wakimoto modules of critical level
162
6.2
Deforming to other levels
167
ix
x
Contents
6.3
Semi-infinite
parabolic
induction
178
6.4 Appendix:
Proof of the Kac-Kazhdan conjecture
189
7
Intertwining operators
192
7.1
Strategy of the proof
192
7.2
The case of si2
197
7.3
Screening operators for an arbitrary
g
205
8
Identification of the center with functions on opers
214
8.1
Description of the center of the vertex algebra
215
8.2
Identification with the algebra of functions on opers
226
8.3
The center of the completed universal enveloping algebra
237
9
Structure of g-modules of critical level
243
9.1
Opers with regular singularity
244
9.2 Nilpotent
opers
247
9.3
Miura opers with regular singularities
256
9.4
Categories of representations of
g
at the critical level
265
9.5
Endomorphisms of the Verma modules
273
9.6
Endomorphisms of the Weyl modules
279
10
Constructing the
Langlands
correspondence
295
10.1
Opers vs. local systems
297
10.2
Harish- Chandra categories
301
10.3
The unramified case
305
10.4
The tamely ramified case
326
10.5
Prom local to global
Langlands
correspondence
353
Appendix
366
A.I Lie algebras
366
A.2 Universal enveloping algebras
366
A.3 Simple Lie algebras
368
A.4 Central extensions
370
A.
5 Affine
Кас
-Moody algebras
371
References
373
Index
377
|
| adam_txt |
Contents
Preface
page
xi
1
Local
Langlands
correspondence
1
1.1
The classical theory
1
1.2 Langlands
parameters over the complex field
9
1.3
Representations of loop groups
18
2
Vertex algebras
31
2.1
The center
31
2.2
Basics of vertex algebras
38
2.3
Associativity in vertex algebras
52
3
Constructing central elements
61
3.1
Segal-Sugawara operators
62
3.2
Lie algebras associated to vertex algebras
70
3.3
The center of a vertex algebra
76
3.4
Jet schemes
81
3.5
The center in the case of sl2
87
4
Opers and the center for a general Lie algebra
101
4.1
Projective
connections, revisited
101
4.2
Opers for a general simple Lie algebra
107
4.3
The center for an arbitrary
affine
Кас
-Moody algebra
117
5
Free field realization
126
5.1
Overview
126
5.2
Finite-dimensional case
128
5.3
The case of
affine
algebras
135
5.4
Vertex algebra interpretation
140
5.5
Computation of the two-cocycle
145
5.6
Comparison of cohomology classes
151
6
Wakimoto modules
161
6.1
Wakimoto modules of critical level
162
6.2
Deforming to other levels
167
ix
x
Contents
6.3
Semi-infinite
parabolic
induction
178
6.4 Appendix:
Proof of the Kac-Kazhdan conjecture
189
7
Intertwining operators
192
7.1
Strategy of the proof
192
7.2
The case of si2
197
7.3
Screening operators for an arbitrary
g
205
8
Identification of the center with functions on opers
214
8.1
Description of the center of the vertex algebra
215
8.2
Identification with the algebra of functions on opers
226
8.3
The center of the completed universal enveloping algebra
237
9
Structure of g-modules of critical level
243
9.1
Opers with regular singularity
244
9.2 Nilpotent
opers
247
9.3
Miura opers with regular singularities
256
9.4
Categories of representations of
g
at the critical level
265
9.5
Endomorphisms of the Verma modules
273
9.6
Endomorphisms of the Weyl modules
279
10
Constructing the
Langlands
correspondence
295
10.1
Opers vs. local systems
297
10.2
Harish- Chandra categories
301
10.3
The unramified case
305
10.4
The tamely ramified case
326
10.5
Prom local to global
Langlands
correspondence
353
Appendix
366
A.I Lie algebras
366
A.2 Universal enveloping algebras
366
A.3 Simple Lie algebras
368
A.4 Central extensions
370
A.
5 Affine
Кас
-Moody algebras
371
References
373
Index
377 |
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| discipline | Mathematik |
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| language | English |
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| spelling | Frenkel, Edward 1968- Verfasser (DE-588)173510116 aut Langlands correspondence for loop groups Edward Frenkel Cambridge ; New York ; Melbourne ; New Delhi ; Singapore Cambridge University Press 2007 © 2007 xvi, 379 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 103 Loops (Group theory) Loop (DE-588)4168153-8 gnd rswk-swf Automorphe Darstellung (DE-588)4192856-8 gnd rswk-swf Loop (DE-588)4168153-8 s Automorphe Darstellung (DE-588)4192856-8 s DE-604 Erscheint auch als Online-Ausgabe Cambridge studies in advanced mathematics 103 (DE-604)BV000003678 103 http://www.loc.gov/catdir/enhancements/fy0803/2007298499-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0803/2007298499-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0803/2007298499-t.html Table of contents only Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frenkel, Edward 1968- Langlands correspondence for loop groups Cambridge studies in advanced mathematics Loops (Group theory) Loop (DE-588)4168153-8 gnd Automorphe Darstellung (DE-588)4192856-8 gnd |
| subject_GND | (DE-588)4168153-8 (DE-588)4192856-8 |
| title | Langlands correspondence for loop groups |
| title_auth | Langlands correspondence for loop groups |
| title_exact_search | Langlands correspondence for loop groups |
| title_exact_search_txtP | Langlands correspondence for loop groups |
| title_full | Langlands correspondence for loop groups Edward Frenkel |
| title_fullStr | Langlands correspondence for loop groups Edward Frenkel |
| title_full_unstemmed | Langlands correspondence for loop groups Edward Frenkel |
| title_short | Langlands correspondence for loop groups |
| title_sort | langlands correspondence for loop groups |
| topic | Loops (Group theory) Loop (DE-588)4168153-8 gnd Automorphe Darstellung (DE-588)4192856-8 gnd |
| topic_facet | Loops (Group theory) Loop Automorphe Darstellung |
| url | http://www.loc.gov/catdir/enhancements/fy0803/2007298499-b.html http://www.loc.gov/catdir/enhancements/fy0803/2007298499-d.html http://www.loc.gov/catdir/enhancements/fy0803/2007298499-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT frenkeledward langlandscorrespondenceforloopgroups |