LEADER 03858nam 2200673 a 450 001 9910452554703321 005 20200520144314.0 010 $a981-4522-20-1 035 $a(CKB)2550000001107675 035 $a(EBL)1336548 035 $a(OCoLC)855505002 035 $a(SSID)ssj0001058912 035 $a(PQKBManifestationID)12394303 035 $a(PQKBTitleCode)TC0001058912 035 $a(PQKBWorkID)11079960 035 $a(PQKB)11505367 035 $a(MiAaPQ)EBC1336548 035 $a(WSP)00008882 035 $a(PPN)189428511 035 $a(Au-PeEL)EBL1336548 035 $a(CaPaEBR)ebr10742823 035 $a(CaONFJC)MIL508334 035 $a(EXLCZ)992550000001107675 100 $a20130816d2013 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBombay Lectures on highest weight representations of infinite dimensional lie algebras$b[electronic resource] /$fVictor G. Kac, Ashok K. Raina, Natasha Rozhkovskaya 205 $a2nd ed. 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$d2013 215 $a1 online resource (250 p.) 225 0$aAdvanced series in mathematical physics ;$vv. 29 300 $aDescription based upon print version of record. 311 $a981-4522-18-X 311 $a1-299-77083-5 320 $aIncludes bibliographical references and index. 327 $aPreface; Preface to the second edition; CONTENTS; Lecture 1; 1.1. The Lie algebra d of complex vector fields on the circle; 1.2. Representations V?,? 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 327 $a11.3. 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 327 $a14.2. Normal ordered product 330 $aThe first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl 8 of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kas 410 0$aAdvanced series in mathematical physics ;$vv. 29. 606 $aLie algebras 606 $aQuantum theory 608 $aElectronic books. 615 0$aLie algebras. 615 0$aQuantum theory. 676 $a520 700 $aKac$b Victor G.$f1943-$044572 701 $aRaina$b Ashok K$044573 701 $aRozhkovskaya$b Natasha$0880648 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910452554703321 996 $aBombay Lectures on highest weight representations of infinite dimensional lie algebras$91966902 997 $aUNINA