Bombay lectures on highest weight representations of infinite dimensional lie algebras.

Format:

Book

Author/Creator:

Kac, Victor G., 1943-

Raina, A. K., author.

Rozhkovskaya, Natasha, author.

Series:

Advanced series in mathematical physics ; v. 29.

Advanced series in mathematical physics ; v. 29

Advanced series in mathematical physics ; vol. 29

Gale eBooks

Language:

English

Subjects (All):

Infinite dimensional Lie algebras.

Quantum field theory.

Physical Description:

1 online resource (xii, 237 pages).

Edition:

2nd ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, 2013.

New Jersey : World Scientific, [2013]

Language Note:

English

Summary:

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

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789814522205

9814522201

OCLC:

855505002