Bombay lectures on highest weight representations of infinite dimensional lie algebras:
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of t...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c1987
|
| Schriftenreihe: | Advanced series in mathematical physics
vol. 29 |
| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveroeffentlichers |
| Zusammenfassung: | This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These algebras appear in the lectures twice, in the reduction theory of soliton equations (KP - KdV) and in the Sugawara construction as the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite-dimensional Lie algebras; and to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory. |
| Beschreibung: | ix, 145 p. ill |
| ISBN: | 9789812798404 |
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| 490 | 0 | |a Advanced series in mathematical physics |v vol. 29 | |
| 520 | |a This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These algebras appear in the lectures twice, in the reduction theory of soliton equations (KP - KdV) and in the Sugawara construction as the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite-dimensional Lie algebras; and to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory. | ||
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| author | Kac, Victor G. 1943- |
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| discipline | Mathematik |
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| id | DE-604.BV044635948 |
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| indexdate | 2024-07-10T07:57:48Z |
| institution | BVB |
| isbn | 9789812798404 |
| language | English |
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| physical | ix, 145 p. ill |
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| spelling | Kac, Victor G. 1943- Verfasser aut Bombay lectures on highest weight representations of infinite dimensional lie algebras Victor G. Kac, Ashok K. Raina Highest weight representation of infinite dimensional lie algebras Singapore World Scientific Pub. Co. c1987 ix, 145 p. ill txt rdacontent c rdamedia cr rdacarrier Advanced series in mathematical physics vol. 29 This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These algebras appear in the lectures twice, in the reduction theory of soliton equations (KP - KdV) and in the Sugawara construction as the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite-dimensional Lie algebras; and to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory. Lie algebras Mathematical physics Quantum field theory Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 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 1\p DE-604 Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s 2\p DE-604 3\p DE-604 Soliton (DE-588)4135213-0 s DE-604 Raina, A. K. Sonstige oth Erscheint auch als Druck-Ausgabe 9971503956 Erscheint auch als Druck-Ausgabe 9971503964 http://www.worldscientific.com/worldscibooks/10.1142/0476#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kac, Victor G. 1943- Bombay lectures on highest weight representations of infinite dimensional lie algebras Lie algebras Mathematical physics Quantum field theory Darstellungstheorie (DE-588)4148816-7 gnd Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd Soliton (DE-588)4135213-0 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Lie-Algebra (DE-588)4130355-6 gnd Dominantes Gewicht (DE-588)4150405-7 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4434344-9 (DE-588)4135213-0 (DE-588)4128289-9 (DE-588)4130355-6 (DE-588)4150405-7 |
| title | Bombay lectures on highest weight representations of infinite dimensional lie algebras |
| title_alt | Highest weight representation 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 Victor G. Kac, Ashok K. Raina |
| title_fullStr | Bombay lectures on highest weight representations of infinite dimensional lie algebras Victor G. Kac, Ashok K. Raina |
| title_full_unstemmed | Bombay lectures on highest weight representations of infinite dimensional lie algebras Victor G. Kac, Ashok 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 algebras Mathematical physics Quantum field theory Darstellungstheorie (DE-588)4148816-7 gnd Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd Soliton (DE-588)4135213-0 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Lie-Algebra (DE-588)4130355-6 gnd Dominantes Gewicht (DE-588)4150405-7 gnd |
| topic_facet | Lie algebras Mathematical physics Quantum field theory Darstellungstheorie Unendlichdimensionale Lie-Algebra Soliton Darstellung Mathematik Lie-Algebra Dominantes Gewicht |
| url | http://www.worldscientific.com/worldscibooks/10.1142/0476#t=toc |
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