| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910779990203321 |
|
|
Autore |
Kac Victor G. <1943-> |
|
|
Titolo |
Bombay lectures on highest weight representations of infinite dimensional lie algebras |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Singapore ; ; Hackensack, N.J., : World Scientific, 2013 |
|
New Jersey : , : World Scientific, , [2013] |
|
�2013 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[2nd ed.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (xii, 237 pages) |
|
|
|
|
|
|
Collana |
|
Advanced series in mathematical physics ; ; vol. 29 |
Gale eBooks |
Advanced series in mathematical physics ; ; v. 29 |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Infinite dimensional Lie algebras |
Quantum field theory |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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 |
|
|
|
|
|
|
|
| |