Support of Virasoro unitarizing measures
Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 621-626.

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.

Une mesure unitarisante de l'algèbre de Virasoro est une mesure de probabilité telle que l'espace L2 associé contienne un sous-espace fermé de fonctionnelles holomorphes sur lequel l'algèbre de Virasoro agit de façon unitaire. On a caractérisé les mesures unitarisantes par une formule d'intégration par parties qui a été explicitement calculée. Dans cette Note on montre qu'une mesure unitarisante doit être portée par le quotient du groupe des homéomorphismes du cercle par le sous-groupe des transformations de Möbius.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02539-6
Airault, Hélène 1; Malliavin, Paul 2; Thalmaier, Anton 3

1 INSSET, Université de Picardie, 48, rue Raspail, 02100 Saint-Quentin, France
2 10, rue Saint Louis en l'Isle, 75004 Paris, France
3 IAM, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany
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Airault, Hélène; Malliavin, Paul; Thalmaier, Anton. Support of Virasoro unitarizing measures. Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 621-626. doi : 10.1016/S1631-073X(02)02539-6. http://www.numdam.org/articles/10.1016/S1631-073X(02)02539-6/

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