, Volume 80, Issue 3, pp 301-342

Unitary representations of some infinite dimensional groups

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We construct projective unitary representations of (a) Map(S 1;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(S 1;T), whereT is a maximal torus ofG, can be extended to representations of Map(S 1;G),

Communicated by A. Jaffe