Invariant differential operators: Volume 4 AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2019]
|
| Series: | De Gruyter studies in mathematical physics
Volume 53 |
| Subjects: | |
| Online Access: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110609684&searchTitles=true https://www.degruyter.com/doc/cover/9783110609684.jpg Inhaltsverzeichnis |
| Physical Description: | IX, 229 Seiten Illustrationen 24 cm x 17 cm, 545 g |
| ISBN: | 9783110609684 3110609681 |
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MARC
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| 100 | 1 | |a Dobrev, Vladimir K. |e Verfasser |0 (DE-588)1035099098 |4 aut | |
| 245 | 1 | 0 | |a Invariant differential operators |n Volume 4 |p AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras |c Vladimir K. Dobrev |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 300 | |a IX, 229 Seiten |b Illustrationen |c 24 cm x 17 cm, 545 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematical physics |v Volume 53 | |
| 490 | 0 | |a De Gruyter studies in mathematical physics |v ... | |
| 650 | 0 | 7 | |a Affine Algebra |0 (DE-588)4348233-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a AdS-CFT-Korrespondenz |0 (DE-588)7752120-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invarianter Differentialoperator |0 (DE-588)4162210-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Superalgebra |0 (DE-588)4304028-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Virasoro-Algebra |0 (DE-588)4272705-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Invarianter Differentialoperator |0 (DE-588)4162210-8 |D s |
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Record in the Search Index
| _version_ | 1804179542577774592 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
1
RELATIVISTIC
AND
NONRELATIVISTIC
HOLOGRAPHY
*
1
1.1
INTERTWINING
OPERATOR
REALIZATION
OF
EUCLIDEAN
ADS/CFT
CORRESPONDENCE
*
1
1.1.1
PRELIMINARIES
*
1
1.1.2
DE
SITTER
SPACE
FROM
IWASAWA
DECOMPOSITION
*
3
1.1.3
CONFORMAL
FIELD
THEORY
REPRESENTATIONS
*
5
1.1.4
REPRESENTATIONS
ON
DE
SITTER
SPACE
*
8
1.1.5
INTERTWINING
RELATIONS
BETWEEN
CONFORMAL
AND
DE
SITTER
REPRESENTATIONS
*
10
1.2
INTERTWINING
OPERATOR
REALIZATION
OF
ANTI
DE
SITTER
HOLOGRAPHY
*
22
1.2.1
PRELIMINARIES
*
22
1.2.2
EIGENVALUE
PROBLEM
AND
TWO-POINT
FUNCTIONS
IN
THE
BULK
*
27
1.2.3
BULK-BOUNDARY
CORRESPONDENCE
*
30
1.2.4
INTERTWINING
PROPERTIES
*
34
1.3
NONRELATIVISTIC
HOLOGRAPHY
*
37
1.3.1
PRELIMINARIES
*
37
1.3.2
TRIANGULAR DECOMPOSITION
OF
5(N)
*
41
1.3.3
CHOICE
OF
BULK
AND
BOUNDARY
*
41
1.3.4
ONE-DIMENSIONAL
CASE
*
43
1.3.5
BOUNDARY-TO-BULK
CORRESPONDENCE
*
45
1.3.6
NONRELATIVISTIC
REDUCTION
*
48
2
NON
RELATIVISTIC
INVARIANT
DIFFERENTIAL
OPERATORS
AND
EQUATIONS
*
51
2.1
NON
RELATIVISTIC
INVARIANT
DIFFERENTIAL
EQUATIONS
FOR
5(1)
*
51
2.1.1
CANONICAL
PROCEDURE
*
51
2.1.2
VERMA
MODULESAND
SINGULAR
VECTORS
*
52
2.1.3
GENERALIZED
SCHRODINGER
EQUATIONS
FROM
A
VECTOR-FIELD
REALIZATION
OF
THE
SCHRODINGER
ALGEBRA
*
58
2.1.4
GENERALIZED
SCHRODINGER
EQUATIONS
IN
THE
BULK
*
60
2.2
NON
RELATIVISTIC
INVARIANT
DIFFERENTIAL
EQUATIONS
FOR
ARBITRARY
N
*
62
2.2.1
GAUSS
DECOMPOSITION
OF
THE
SCHRODINGER
GROUP
*
62
2.2.2
REPRESENTATIONS
OF
S(N)
*
63
2.2.3
SINGULAR
VECTORS
AND
INVARIANT
EQUATIONS
FOR
5(2
N)
*
69
2.2.4
SINGULAR
VECTORS
AND
INVARIANT
EQUATIONS
FOR
5(2A/
+
1)
*
71
2.3
NON
RELATIVISTIC
INVARIANT
EQUATIONS
FOR
5(3)
*
73
2.3.1
ALGEBRAIC
STRUCTURE
AND
ACTIONS
*
73
2.3.2
SINGULAR
VECTORS
*
76
VIII
*
CONTENTS
2.3.3
2.4
2.4.1
2.4.2
2.4.3
2.5
2.5.1
2.5.2
2.5.3
2.5.4
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.7.1
3.7.2
3.7.3
3.8
3.8.1
3.8.2
3.8.3
3.8.4
3.8.5
3.9
3.9.1
3.9.2
3.9.3
3.9.4
NON-RELATIVISTIC
EQUATIONS
*
79
Q-SCHRDDINGER
ALGEBRA
*
79
Q-DEFORMATION
OF
THE
SCHRODINGER
ALGEBRA
*
79
LOWEST
WEIGHT
MODULES
OF
5^(1)
-----
80
VECTOR-FIELD
REALIZATION
OF
S
Q
(L)
AND
GENERALIZED
Q-DEFORMED
HEAT
EQUATIONS
*
83
DIFFERENCE
ANALOGUES
OF
THE
FREE
SCHRODINGER
EQUATION
*
85
MOTIVATIONS
-----
85
DEFINITION
AND
NOTATION
*
87
CONSTRUCTION
OF
A
REALIZATION
OF
5
*
88
INVARIANT
FINITE
DIFFERENCE
EQUATIONS
*
89
VIRASORO
ALGEBRA
AND
SUPER-VIRASORO
ALGEBRAS
*
91
PRELIMINARIES
ON
VIRASORO
AND
N
=
1
SUPER-VIRASORO
ALGEBRAS
*
92
UNITARITY
-----
96
MULTIPLET
CLASSIFICATION
OF
THE
REDUCIBLE
(GENERALIZED)
VERMA
MODULES
-----
97
CHARACTERS
OF
(GENERALIZED)
HIGHEST
WEIGHT
MODULES
*
104
WEYL
GROUP
FOR
VIRASORO
AND
N
=
1
SUPER-VIRASORO
ALGEBRAS
*
106
FOCK
MODULES
OVER
THE
VIRASORO
ALGEBRA
*
111
CHARACTERS
OF
THE
UNITARIZABLE
HIGHEST
WEIGHT
MODULES
OVER
THE
N
=
2
SUPERCONFORMAL
ALGEBRAS
*
116
PRELIMINARIES
*
116
HIGHEST
WEIGHT
MODULES,
REDUCIBILITY,
UNITARITY
*
116
CHARACTER
FORMULAE
*
118
MODULAR
INVARIANTS
FOR
THETA-FUNCTIONS
WITH
CHARACTERISTICS
AND
THE
TWISTED
N
=
2
SUPERCONFORMAL
AND
SU(2)
KAC-MOODY
ALGEBRAS
*
122
PRELIMINARIES
*
122
CHARACTERS
OF
THE
TWISTED
N
=
2
SUPERCONFORMAL
AND
SU(2)
KAC-MOODY
ALGEBRAS
*
122
MODULAR
INVARIANTS
FOR
9-FUNCTIONS
WITH
CHARACTERISTICS
*
125
MODULAR
INVARIANT
PARTITION
FUNCTIONS
*
129
APPENDIX
*
130
CLASSIFICATION
OF
MODULAR
INVARIANT
PARTITION
FUNCTIONS
FOR
THE
TWISTED
N
=
2
SUPERCONFORMAL
ALGEBRA,
TWISTED
SU(2)
KAC-MOODY
ALGEBRA
AND
D
2
K
PARAFERMIONS
*
132
PRELIMINARIES
*
132
PARAFERMIONS,
SU(2),
N
=
2
AND
THE
UNTWISTED
LINE
OF
CONFORMAL
MODELS
*
132
TWISTED
SECTOR
OF
N
=
2
AND
SU(2)
AND
C-DISORDER
FIELDS
*
135
MODULAR
INVARIANTS
FOR
THE
Z
2
ORBIFOLD
LINE
*
137
CONTENTS
*
IX
4
AFFINE
LIE
(SUPER-)ALGEBRAS
*
143
4.1
MULTIPLET
CLASSIFICATION
OF
VERMA
MODULES
OVER
AFFINE
LIE
ALGEBRAS
AND
INVARIANT
DIFFERENTIAL
OPERATORS:
THE
A^
EXAMPLE
*
144
4.1.1
DEFINITIONS
AND
NOTATION
-----
144
4.1.2
MULTIPLETS
OF
REDUCIBLE
VERMA
MODULES,
IMAGINARY
REFLECTIONS
AND
EXTENDED
WEYL
GROUP
*
145
4.1.3
MULTIPLET
CLASSIFICATION
IN
THE
CASE
*
147
4.1.4
THE
A^
Y
CASE
-----
150
4.1.5
THE
VIRASORO-A^
CORRESPONDENCE
*
153
4.1.6
THE
A^
Y
CASE
-----
157
4.2
NEW
WEYL
GROUPS
FOR
A^
Y
AND
CHARACTERS
OF
SINGULAR
HIGHEST
WEIGHT
MODULES
*
160
4.2.1
INTRODUCTION
-----
161
4.2.2
SINGULAR
VERMA
MODULES
OVER
A^
*
162
4.2.3
CALCULATION
OF
CHARACTERS
*
163
4.2.4
WEYL
GROUPS
FOR
THE
SINGULAR
HIGHEST
WEIGHT
MODULES
*
170
4.2.5
DISCUSSION
-----
174
4.3
SPECIAL
REPRESENTATION
OF
THE
S0(3,
2)
KAC-MOODY
ALGEBRA
*
175
4.3.1
INTRODUCTION
*
175
4.3.2
PRELIMINARIES
-----
177
4.3.3
LOWEST
WEIGHT
REPRESENTATIONS
OF
G
AND
G
*
180
4.3.4
NULL
VECTORS
AND
REDUCED
WEYL
GROUPS
*
183
4.3.5
SUMMARY
-----
190
4.4
MULTIPLETS
OF
VERMA
MODULES
OVER
THE
OSP(2,2)
(1)
SUPER
KAC-MOODY
ALGEBRA
*
190
4.4.1
DEFINITIONS
AND
NOTATION
*
190
4.4.2
VERMA
MODULES,
THEIR
REDUCIBILITY
AND
MULTIPLETS
*
192
4.4.3
VERMA
MODULES
WITH
NONSINGULAR
INTEGRAL
HIGHEST
WEIGHTS
*
193
4.4.4
VERMA
MODULES
WITH
SINGULAR
HIGHEST
WEIGHTS
*
195
EPILOGUE
*
197
W
ALGEBRAS
*
197
YANGIANS
-----
197
CLUSTER
ALGEBRAS
AND
QUIVERS
*
197
BIBLIOGRAPHY
*
199
AUTHOR
INDEX
*
231
SUBJECT
INDEX
*
233
|
| any_adam_object | 1 |
| author | Dobrev, Vladimir K. |
| author_GND | (DE-588)1035099098 |
| author_facet | Dobrev, Vladimir K. |
| author_role | aut |
| author_sort | Dobrev, Vladimir K. |
| author_variant | v k d vk vkd |
| building | Verbundindex |
| bvnumber | BV045560385 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)1032350361 (DE-599)DNB1156287235 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV045560385 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:21:31Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110609684 3110609681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030944183 |
| oclc_num | 1032350361 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-83 |
| physical | IX, 229 Seiten Illustrationen 24 cm x 17 cm, 545 g |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematical physics |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Dobrev, Vladimir K. Verfasser (DE-588)1035099098 aut Invariant differential operators Volume 4 AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras Vladimir K. Dobrev Berlin ; Boston De Gruyter [2019] IX, 229 Seiten Illustrationen 24 cm x 17 cm, 545 g txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics Volume 53 De Gruyter studies in mathematical physics ... Affine Algebra (DE-588)4348233-8 gnd rswk-swf AdS-CFT-Korrespondenz (DE-588)7752120-1 gnd rswk-swf Invarianter Differentialoperator (DE-588)4162210-8 gnd rswk-swf Superalgebra (DE-588)4304028-7 gnd rswk-swf Virasoro-Algebra (DE-588)4272705-4 gnd rswk-swf Invarianter Differentialoperator (DE-588)4162210-8 s AdS-CFT-Korrespondenz (DE-588)7752120-1 s Virasoro-Algebra (DE-588)4272705-4 s Affine Algebra (DE-588)4348233-8 s Superalgebra (DE-588)4304028-7 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl (DE-604)BV043795240 4 Erscheint auch als 978-3-11-061141-0 Erscheint auch als Online-Ausgabe, PDF 978-3-11-061140-3 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-060971-4 De Gruyter studies in mathematical physics Volume 53 (DE-604)BV040141722 53 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110609684&searchTitles=true X:MVB https://www.degruyter.com/doc/cover/9783110609684.jpg DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030944183&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dobrev, Vladimir K. Invariant differential operators De Gruyter studies in mathematical physics Affine Algebra (DE-588)4348233-8 gnd AdS-CFT-Korrespondenz (DE-588)7752120-1 gnd Invarianter Differentialoperator (DE-588)4162210-8 gnd Superalgebra (DE-588)4304028-7 gnd Virasoro-Algebra (DE-588)4272705-4 gnd |
| subject_GND | (DE-588)4348233-8 (DE-588)7752120-1 (DE-588)4162210-8 (DE-588)4304028-7 (DE-588)4272705-4 |
| title | Invariant differential operators |
| title_auth | Invariant differential operators |
| title_exact_search | Invariant differential operators |
| title_full | Invariant differential operators Volume 4 AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras Vladimir K. Dobrev |
| title_fullStr | Invariant differential operators Volume 4 AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras Vladimir K. Dobrev |
| title_full_unstemmed | Invariant differential operators Volume 4 AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras Vladimir K. Dobrev |
| title_short | Invariant differential operators |
| title_sort | invariant differential operators ads cft super virasoro affine super algebras |
| topic | Affine Algebra (DE-588)4348233-8 gnd AdS-CFT-Korrespondenz (DE-588)7752120-1 gnd Invarianter Differentialoperator (DE-588)4162210-8 gnd Superalgebra (DE-588)4304028-7 gnd Virasoro-Algebra (DE-588)4272705-4 gnd |
| topic_facet | Affine Algebra AdS-CFT-Korrespondenz Invarianter Differentialoperator Superalgebra Virasoro-Algebra |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110609684&searchTitles=true https://www.degruyter.com/doc/cover/9783110609684.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030944183&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV043795240 (DE-604)BV040141722 |
| work_keys_str_mv | AT dobrevvladimirk invariantdifferentialoperatorsvolume4 AT walterdegruytergmbhcokg invariantdifferentialoperatorsvolume4 |