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Autore: | Kac Victor G. <1943-> |
Titolo: | Bombay Lectures on highest weight representations of infinite dimensional lie algebras [[electronic resource] /] / Victor G. Kac, Ashok K. Raina, Natasha Rozhkovskaya |
Pubblicazione: | Singapore ; ; Hackensack, N.J., : World Scientific, 2013 |
Edizione: | 2nd ed. |
Descrizione fisica: | 1 online resource (250 p.) |
Disciplina: | 520 |
Soggetto topico: | Lie algebras |
Quantum theory | |
Soggetto genere / forma: | Electronic books. |
Altri autori: | RainaAshok K RozhkovskayaNatasha |
Note generali: | Description based upon print version of record. |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | 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 | |
Sommario/riassunto: | 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 |
Titolo autorizzato: | Bombay Lectures on highest weight representations of infinite dimensional lie algebras |
ISBN: | 981-4522-20-1 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910452554703321 |
Lo trovi qui: | Univ. Federico II |
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