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