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

  • Roe Goodman
  • Nolan R. Wallach
Conference paper

DOI: 10.1007/978-1-4612-1104-4_4

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 4)
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

Abstract

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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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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