Bombay lectures on highest weight representations of infinite dimensional Lie algebras:
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Singapore [u.a.]
World Scientific
1987
|
Schriftenreihe: | Advanced series in mathematical physics
2 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | IX, 145 S. |
ISBN: | 9971503956 9971503964 |
Internformat
MARC
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245 | 1 | 0 | |a Bombay lectures on highest weight representations of infinite dimensional Lie algebras |c by V. G. Kac ; A. K. Raina |
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490 | 1 | |a Advanced series in mathematical physics |v 2 | |
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650 | 7 | |a Lie, Algèbres de |2 ram | |
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650 | 4 | |a Représentations d'algèbres | |
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Datensatz im Suchindex
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adam_text | CONTENTS
Preface v
Lecture 1 1
1.1. The Lie algebra d of complex vector fields on the circle 1
1.2. Representations Va ^ of d 4
1.3. Central extensions of d: the Virasoro algebra 7
Lecture 2 11
2.1. Definition of positive energy representations of Vir 11
2.2. Oscillator algebra stf 12
2.3. Oscillator representations of Vir 15
Lecture 3 19
3.1. Complete reducibility of the oscillator representations
of Fir 19
3.2. Highest weight representations of Vir 21
3.3. Verma representations M(c, h) and irreducible highest
weight representations V(c, h) of Vir 23
3.4. More (unitary) oscillator representations of Fir 26
Lecture 4 33
4.1. Lie algebras of infinite matrices 33
4.2. Infinite wedge space Fand the Dirac positron theory 35
4.3. Representation oiGL^ andgfi,,, inF. Unitarity of
highest weight representations of gi^ 38
4.4. Representation of „ in F 43
4.5. Representations of Vir in F 45
Lecture 5 49
5.1. Boson fermion correspondence 49
5.2. Wedging and contracting operators 51
5.3. Vertex operators. The first part of the boson fermion
correspondence 53
5.4. Vertex representations ofgS.^ and a^ 56
vii
viii
Lecture 6 59
6.1. Schur polynomials 59
6.2. The second part of the boson fermion correspondence 61
6.3. An application: structure of the Virasoro representations
for c = 1 64
Lecture 7 69
7.1. Orbit of the vacuum vector under GL^ 69
7.2. Defining equations for £2 in F(? 69
7.3. Differential equations for 12 in CfjCj.Xj,...] 71
7.4. Hirota s bilinear equations 72
7.5. KP hierarchy 74
7.6. A^ soliton solutions 77
Lecture 8 81
8.1. Degenerate representations and the determinant
detw(c, h) of the contravariant form 81
8.2. The determinant detn(c, h) as a polynomial in h 83
8.3. The Kac determinant formula 85
8.4. Some consequences of the determinant formula for
unitarity and degeneracy 88
Lecture 9 93
9.1. Representations of loop algebras in a«, 93
9.2. Representations of £i n in F(m) 96
9.3. The invariant bilinear form ongin. The action of
GLn on giln ^ 97
9.4. Reduction from ax to . £„ and unitarity of highest
weight representations of ¦ £„ 100
Lecture 10 105
10.1. Nonabelian generalization of Virasoro operators:
the Sugawara construction 105
10.2. The Goddard Kent Olive construction 113
Lecture 11 117
11.1. 6i2 and its Weyl group 117
11.2. The Weyl Kac character formula and Jacobi Riemann
theta functions 119
ix
11.3. A character identity 124
Lecture 12 129
12.1. Preliminaries on 6£2 129
12.2. A tensor product decomposition of some representations
of 6 130
12.3. Construction and unitarity of the discrete series
representations of Vir 132
12.4. Completion of the proof of the Kac determinant
formula 137
12.5. On non unitarity in the region 0 c l,h 0 138
References 141
|
any_adam_object | 1 |
author | Kac, Victor G. 1943- Raina, A. K. |
author_GND | (DE-588)110066820 |
author_facet | Kac, Victor G. 1943- Raina, A. K. |
author_role | aut aut |
author_sort | Kac, Victor G. 1943- |
author_variant | v g k vg vgk a k r ak akr |
building | Verbundindex |
bvnumber | BV002301552 |
callnumber-first | Q - Science |
callnumber-label | QA252 |
callnumber-raw | QA252.3 |
callnumber-search | QA252.3 |
callnumber-sort | QA 3252.3 |
callnumber-subject | QA - Mathematics |
classification_rvk | SK 340 SK 260 SK 950 |
classification_tum | MAT 173f PHY 012f |
ctrlnum | (OCoLC)18475755 (DE-599)BVBBV002301552 |
dewey-full | 512.55 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512.55 |
dewey-search | 512.55 |
dewey-sort | 3512.55 |
dewey-tens | 510 - Mathematics |
discipline | Physik Mathematik |
format | Book |
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id | DE-604.BV002301552 |
illustrated | Not Illustrated |
indexdate | 2024-07-09T15:43:40Z |
institution | BVB |
isbn | 9971503956 9971503964 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001512574 |
oclc_num | 18475755 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM DE-384 DE-19 DE-BY-UBM DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-11 DE-188 |
owner_facet | DE-91G DE-BY-TUM DE-384 DE-19 DE-BY-UBM DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-11 DE-188 |
physical | IX, 145 S. |
publishDate | 1987 |
publishDateSearch | 1987 |
publishDateSort | 1987 |
publisher | World Scientific |
record_format | marc |
series | Advanced series in mathematical physics |
series2 | Advanced series in mathematical physics |
spelling | Kac, Victor G. 1943- Verfasser (DE-588)110066820 aut Bombay lectures on highest weight representations of infinite dimensional Lie algebras by V. G. Kac ; A. K. Raina Singapore [u.a.] World Scientific 1987 IX, 145 S. txt rdacontent n rdamedia nc rdacarrier Advanced series in mathematical physics 2 Lie, Algèbres de Lie, Algèbres de ram Lie-algebra's gtt Oneindige dimensie gtt Quanta, Théorie des ram Representatie (wiskunde) gtt Représentations d'algèbres Quantentheorie Lie algebras Quantum theory Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Dominantes Gewicht (DE-588)4150405-7 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 s Dominantes Gewicht (DE-588)4150405-7 s Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 s DE-604 Darstellungstheorie (DE-588)4148816-7 s Lie-Algebra (DE-588)4130355-6 s Soliton (DE-588)4135213-0 s Raina, A. K. Verfasser aut Advanced series in mathematical physics 2 (DE-604)BV000900258 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001512574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Kac, Victor G. 1943- Raina, A. K. Bombay lectures on highest weight representations of infinite dimensional Lie algebras Advanced series in mathematical physics Lie, Algèbres de Lie, Algèbres de ram Lie-algebra's gtt Oneindige dimensie gtt Quanta, Théorie des ram Representatie (wiskunde) gtt Représentations d'algèbres Quantentheorie Lie algebras Quantum theory Lie-Algebra (DE-588)4130355-6 gnd Soliton (DE-588)4135213-0 gnd Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Dominantes Gewicht (DE-588)4150405-7 gnd |
subject_GND | (DE-588)4130355-6 (DE-588)4135213-0 (DE-588)4434344-9 (DE-588)4148816-7 (DE-588)4128289-9 (DE-588)4150405-7 |
title | Bombay lectures on highest weight representations of infinite dimensional Lie algebras |
title_auth | Bombay lectures on highest weight representations of infinite dimensional Lie algebras |
title_exact_search | Bombay lectures on highest weight representations of infinite dimensional Lie algebras |
title_full | Bombay lectures on highest weight representations of infinite dimensional Lie algebras by V. G. Kac ; A. K. Raina |
title_fullStr | Bombay lectures on highest weight representations of infinite dimensional Lie algebras by V. G. Kac ; A. K. Raina |
title_full_unstemmed | Bombay lectures on highest weight representations of infinite dimensional Lie algebras by V. G. Kac ; A. K. Raina |
title_short | Bombay lectures on highest weight representations of infinite dimensional Lie algebras |
title_sort | bombay lectures on highest weight representations of infinite dimensional lie algebras |
topic | Lie, Algèbres de Lie, Algèbres de ram Lie-algebra's gtt Oneindige dimensie gtt Quanta, Théorie des ram Representatie (wiskunde) gtt Représentations d'algèbres Quantentheorie Lie algebras Quantum theory Lie-Algebra (DE-588)4130355-6 gnd Soliton (DE-588)4135213-0 gnd Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Dominantes Gewicht (DE-588)4150405-7 gnd |
topic_facet | Lie, Algèbres de Lie-algebra's Oneindige dimensie Quanta, Théorie des Representatie (wiskunde) Représentations d'algèbres Quantentheorie Lie algebras Quantum theory Lie-Algebra Soliton Unendlichdimensionale Lie-Algebra Darstellungstheorie Darstellung Mathematik Dominantes Gewicht |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001512574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000900258 |
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