Abstract
A modified Hamiltonian action of DiffS ~ on the phase space LGC/G c, 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 nonequivarlant moment map, thereby defining a classical Polsson bracket realization of a central extension of the Lie algebra diff c S t . The resulting formula expresses the Diff S 1 generators in terms of the left LG translation generators, giving a shifted modification of both the classical and quantum versions of the Sugawara formula.
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