03511oam 2200553 450 991077999020332120190911112729.0981-4522-20-1(OCoLC)855505002(MiFhGG)GVRL8RFP(EXLCZ)99255000000110767520130930h20132013 uy 0engurun|---uuuuatxtccrBombay lectures on highest weight representations of infinite dimensional lie algebras2nd ed.Singapore ;Hackensack, N.J. World Scientific2013New Jersey :World Scientific,[2013]�20131 online resource (xii, 237 pages)Advanced series in mathematical physics ;vol. 29Gale eBooksAdvanced series in mathematical physics ;v. 29Description based upon print version of record.981-4522-18-X 1-299-77083-5 Includes bibliographical references and index.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 Vir11.3. 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 fields14.2. Normal ordered productThe 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, KasAdvanced series in mathematical physics ;v. 29.Infinite dimensional Lie algebrasQuantum field theoryInfinite dimensional Lie algebras.Quantum field theory.520Kac Victor G.1943-44572Raina A. K.Rozhkovskaya NatashaMiFhGGMiFhGGBOOK9910779990203321Bombay Lectures on highest weight representations of infinite dimensional lie algebras3861277UNINA