Positive-Energy Representations of the Group of Diffeomorphisms of the Circle
- Cite this paper as:
- Goodman R., Wallach N.R. (1985) Positive-Energy Representations of the Group of Diffeomorphisms of the Circle. In: Kac V. (eds) Infinite Dimensional Groups with Applications. Mathematical Sciences Research Institute Publications, vol 4. Springer, New York, NY
Let D be the group of orientation-preserving diffeomorphisms of the circle S1. Then D is Fréchet Lie group with Lie algebra (d∞)ℝ the smooth real vector fields on S1. Let dℝ be the subalgebra of real vector fields with finite Fourier series. This lecture outlines a proof that every infinitesimally unitary projective positive-energy representation of dℝ integrates to a continuous projective unitary representation of D. This result was conjectured by V. Kac.
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