LEADER 04273nam 2200613Ia 450 001 9910825441603321 005 20200520144314.0 010 $a9786611956356 010 $a1-281-95635-X 010 $a981-281-070-6 035 $a(CKB)1000000000538118 035 $a(StDuBDS)AH24685569 035 $a(SSID)ssj0000190865 035 $a(PQKBManifestationID)11178479 035 $a(PQKBTitleCode)TC0000190865 035 $a(PQKBWorkID)10180267 035 $a(PQKB)10792869 035 $a(MiAaPQ)EBC1681623 035 $a(WSP)00004269 035 $a(Au-PeEL)EBL1681623 035 $a(CaPaEBR)ebr10255678 035 $a(CaONFJC)MIL195635 035 $a(OCoLC)815755950 035 $a(EXLCZ)991000000000538118 100 $a20011218d2001 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on infinite-dimensional Lie algebra /$fMinoru Wakimoto 205 $a1st ed. 210 $aRiver Edge, N.J. $cWorld Scientific$d2001 215 $ax, 444 p 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-02-4129-1 311 $a981-02-4128-3 320 $aIncludes bibliographical references (p. 429-440) and index. 327 $a1. Preliminaries on affine Lie algebras. 1.1. Affine Lie algebras. 1.2. Extended affine Weyl group. 1.3. Some formulas for finite-dimensional simple Lie algebras -- 2. Characters of integrable representations. 2.1. Weyl-Kac character formula. 2.2. Specialized characters. 2.3. Product expression of characters. 2.4. Modular transformation -- 3. Principal admissible weights. 3.1. Admissible weights. 3.2. Principal admissible weights. 3.3. Characters of principal admissible representations. 3.4. Parametrization of principal admissible weights. 3.5. Modular transformation -- 4. Residue of principal admissible characters. 4.1. Non-degenerate principal admissible weights. 4.2. Modular transformation of residue. 4.3. Fusion coefficients -- 5. Characters of affine orbifolds. 5.1. Characters of finite groups. 5.2. Fusion datum. 5.3. Characters of affine orbifolds -- 6. Operator calculus. 6.1. Operator products. 6.2. Boson-fermion correspondence -- 7. Branching functions. 7.1. Virasoro modules. 7.2. Virasoro modules of central charge-[symbol]. 7.3. Branching functions. 7.4. Tensor product decomposition -- 8. W-algebra. 8.1. Free fermionic fields [symbol](z) and [symbol](z). 8.2. Free fermionic fields [symbol](z) and [symbol](z). 8.3. Ghost field associated to a simple Lie algebra. 8.4. BRST complex. 8.5. Euler-Poincaré characteristics -- 9. Vertex representations for affine Lie algebras. 9.1. Simple examples of vertex operators. 9.2. Basic representations of [symbol](2, C). 9.3. Construction of basic representation -- 10. Soliton equations. 10.1. Hirota bilinear differential operators. 10.2. KdV equation and Hirota bilinear differential equations. 10.3. Hirota equations associated to the basic representation. 10.4. Non-linear Schrödinger equations. 330 $aThe representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G. Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations. 517 3 $aInfinite-dimensional Lie algebra 606 $aInfinite dimensional Lie algebras 606 $aLie algebras 615 0$aInfinite dimensional Lie algebras. 615 0$aLie algebras. 676 $a512/.482 700 $aWakimoto$b Minoru$f1942-$066934 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910825441603321 996 $aLectures on infinite-dimensional Lie algebra$91103903 997 $aUNINA