Abstract
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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References
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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. https://doi.org/10.1007/978-1-4612-1104-4_4
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DOI: https://doi.org/10.1007/978-1-4612-1104-4_4
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