Positive-Energy Representations of the Group of Diffeomorphisms of the Circle

  • Roe Goodman
  • Nolan R. Wallach
Conference paper
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 4)


Let D be the group of orientation-preserving diffeomorphisms of the circle S1. Then D is Fréchet Lie group with Lie algebra (d) the smooth real vector fields on S1. Let d 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 d integrates to a continuous projective unitary representation of D. This result was conjectured by V. Kac.


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    Goodman, R., and Wallach, N. R., Projective Unitary Positive-Energy Representations of Diff(S1), J. Functional Analysis (to appear).Google Scholar
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Roe Goodman
    • 1
  • Nolan R. Wallach
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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