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Record Nr. |
UNINA9910452554703321 |
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Autore |
Kac Victor G. <1943-> |
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Titolo |
Bombay Lectures on highest weight representations of infinite dimensional lie algebras [[electronic resource] /] / Victor G. Kac, Ashok K. Raina, Natasha Rozhkovskaya |
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Pubbl/distr/stampa |
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Singapore ; ; Hackensack, N.J., : World Scientific, 2013 |
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ISBN |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (250 p.) |
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Collana |
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Advanced series in mathematical physics ; ; v. 29 |
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Altri autori (Persone) |
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RainaAshok K |
RozhkovskayaNatasha |
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Disciplina |
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Soggetti |
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Lie algebras |
Quantum theory |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Preface; Preface to the second edition; CONTENTS; Lecture 1; 1.1. The Lie algebra d of complex vector fields on the circle; 1.2. Representations Vα,β of; 1.3. Central extensions of : the Virasoro algebra; Lecture 2; 2.1. Definition of positive-energy representations of Vir; 2.2. Oscillator algebra A; 2.3. Oscillator representations of Vir; Lecture 3; 3.1. Complete reducibility of the oscillator representations of Vir; 3.2. Highest weight representations of Vir; 3.3. Verma representations M(c, h) and irreducible highest weight representations V (c, h) of Vir |
11.3. A character identity Lecture 12; 12.1. Preliminaries on sl2; 12.2. A tensor product decomposition of some representations of sl2; 12.3. Construction and unitarity of the discrete series representations of Vir; 12.4. Completion of the proof of the Kac determinant formula; 12.5. On non-unitarity in the region 0 c < 1, h 0; Lecture 13; 13.1. Formal distributions; 13.2. Local pairs of formal distributions; 13.3. Formal Fourier transform; 13.4. Lambda-bracket of local formal distributions; Lecture 14; 14.1. Completion of U, restricted representations and quantum fields |
14.2. Normal ordered product |
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Sommario/riassunto |
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The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. 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 8 of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kas |
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