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

* Final gross prices may vary according to local VAT.

Get Access


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.