Letters in Mathematical Physics

, Volume 19, Issue 4, pp 277–283 | Cite as

Twisted Diff S1-action on loop groups and representations of the virasoro algebra

  • J. Harnad
  • B. A. Kupershmidt


A modified Hamiltonian action of Diff S1on the phase space LG C /GC, where LG is a loop group, is defined by twisting the usual action by a left translation in LG. This twisted action is shown to be generated by a nonequivariant moment map, thereby defining a classical Poisson bracket realization of a central extension of the Lie algebra diffCS1. The resulting formula expresses the Diff S1generators in terms of the left LG translation generators, giving a shifted modification of both the classical and quantum versions of the Sugawara formula.

AMS subject classifications (1980)

58Bxx 58Fxx 


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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • J. Harnad
    • 1
  • B. A. Kupershmidt
    • 2
  1. 1.Centre de recherches mathématiquesUniversité de MontréalMontréalCanada
  2. 2.The University of Tennessee Space InstituteTullahomaUSA

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