Support of Virasoro unitarizing measuresSupport des mesures unitarisantes de l'algèbre de Virasoro

A unitarizing measure is a probability measure such that the associated L² space contains a closed subspace of holomorphic functionals on which the Virasoro algebra acts unitarily. It has been shown that the unitarizing property is equivalent to an a priori given formula of integration by parts, which has been computed explicitly. We show in this Note that unitarizing measures must be supported by the quotient of the homeomorphism group of the circle by the subgroup of Möbius transformations. To cite this article: H. Airault et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 621–626.