Communications in Mathematical Physics

, Volume 80, Issue 3, pp 301–342 | Cite as

Unitary representations of some infinite dimensional groups

  • Graeme Segal


We construct projective unitary representations of (a) Map(S1;G), the group of smooth maps from the circle into a compact Lie groupG, and (b) the group of diffeomorphisms of the circle. We show that a class of representations of Map(S1;T), whereT is a maximal torus ofG, can be extended to representations of Map(S1;G),


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Graeme Segal
    • 1
  1. 1.St. Catherine's CollegeOxford UniversityOxfordEngland

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