Generalization of the Sugawara Construction

  • Jean Thierry-Mieg
Part of the NATO ASI Series book series (NSSB, volume 185)


An outstanding problem in the theory of Kac Moody algebras is to try and generalize as many properties of the finite dimensional Lie algebras as possible to the affine case. The beauty of the theory is that this is often feasible and yields a great wealth of results in arithmetics and quantum field theory.


Weyl Group Group Index Primary Field Virasoro Algebra Dual Coxeter Number 
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  1. 1a.
    V.G. Kac, Infinite dimensional Lie algebras, chapter 2, Cambridge, Univerity Press, 1985.Google Scholar
  2. 1b.
    P. Goddard & D. Olive, Int.J.Mod.Phys. A1 (1986) 303.MathSciNetADSGoogle Scholar
  3. 2a.
    Yen Chih Ta, Comptes Rendus Acad.Sc.Paris 228 (1949) 628–630.MATHGoogle Scholar
  4. 2b.
    C. Chevalley, Proc.Int.Congress Math., Cambridge Mass. 1950 11 (1952) 21-24.Google Scholar
  5. 2c.
    G. Racah, Lincei Rend.Sc.Fis.Mat.Nat. 8 (1950) 108–112.MathSciNetMATHGoogle Scholar
  6. 3.
    A.B. Zamolodchikov, Theor.Math.Phys. 65 (1985) 1205.MathSciNetCrossRefGoogle Scholar
  7. 4.
    V.A. Fateev & A.B. Zamolodchikov, Nucl.Phys. B280 (1987) 644.MathSciNetADSCrossRefGoogle Scholar
  8. 5.
    F.A.Bais, P.Bouwknegt, K.Schoutens & M.Surridge, Amsterdam preprints ITFA 87-12 & 87-21, 1987.Google Scholar
  9. 6.
    A.Borel & C. Chevalley, Mem.Am.Math.Soc. 14 (1955) 1.MathSciNetMATHGoogle Scholar
  10. 7.
    E. Witt, Abh.Math.Sem.Hansischen Univ. 14 (1941) 289.MathSciNetCrossRefGoogle Scholar
  11. 8.
    C. Itzykson, Int.J.Mod.Phys. A1 (1986) 65.MathSciNetADSGoogle Scholar
  12. 9.
    P.Cvitanovic, Group Theory, NORDITA classics illustrated, 1984.Google Scholar
  13. 10.
    P. Goddard, A. Kent & D. Olive, Phys.Lett. B152 (1985) 88.MathSciNetADSGoogle Scholar
  14. 11.
    J. Thierry-Mieg, Phys.Lett. B197 (1987) 368.MathSciNetADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Jean Thierry-Mieg
    • 1
    • 2
  1. 1.Department of Applied MathematicsCNRS and Royal Society European exchange programUK
  2. 2.Theoretical Physics University of CambridgeCambridgeUK

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