Support of Virasoro unitarizing measures.
type: Item
instance of: scholarly article
title: Support of Virasoro unitarizing measures.
zbMATH Open document ID: 1033.58030
DOI: 10.1016/S1631-073X(02)02539-6
author: Paul Malliavin
author: Anton Thalmaier
author: Hélène Airault
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-12-04T00:00:00Z
review text: It is studied a unitarizing measure of the Virasoro algebra as a probability measure for which the associated space \(L^2\) contains a closed subspace of holomorphic functionals on which this algebra acts unitarily. It is taken into account that the unitarizing property is equivalent to an a priori given formula of integration by parts, which has been previously computed explicitly [\textit{H. Airault} and \textit{P. Malliavin}, J. Math. Pures Appl., IX. Sér. 80, 627--667 (2001; Zbl 1032.58021)]. In addition, it is shown that the unitarizing measures must be supported by the quotient of the homeomorphism group on the circle by the subgroup \(\text{SL}(2,\mathbb{R})\) of Möbius transformations. The work is stimulated by previous investigations related to the canonical Brownian motion on the group diffeomorphisms of the circle [\textit{P. Malliavin}, C. R. Acad. Sci., Paris, Sér. I, Math. 329, 325--329 (1999; Zbl 1006.60073); \textit{H. Airault} and \textit{J. Ren}, J. Funct. Anal. 196, 395--426 (2000; Zbl 1023.60051)] and to the probability measures for representations of Virasoro algebras [\textit{H. Airault}, C. R., Math., Acad. Sci. Paris 334, 787--792 (2002; Zbl 1008.58025)].
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 17B68
zbMATH DE Number: 1850791
zbMATH Keywords: Möbius transformations
zbMATH Keywords: unitarizing measure
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: homeomorphism group on the circle
reviewed by: A. A. Bogush
MaRDI profile type: Publication
cites work: Unitarizing measure: The Heisenberg algebra, the Virasoro algebra
cites work: Unitarizing probability measures for representations of Virasoro algebra
cites work: Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle''
cites work: The Ricci curvature of Diff S1/SL(2, R)
cites work: Canonical Brownian motion on the diffeomorphism group of the circle
cites work: The canonic diffusion above the diffeomorphism group of the circle
cites work: Integration on loop groups. III: Asymptotic Peter-Weyl orthogonality
full work available at URL: s1631-073x(02)02539-6
OpenAlex ID: W2020499423
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description: scientific article; zbMATH DE number 1850791