The orbit method and the Virasoro extension of \(\text{diff}^+(S^1)\). I: Orbital integrals
type: Item
instance of: scholarly article
title: The orbit method and the Virasoro extension of \(\text{diff}^+(S^1)\). I: Orbital integrals
zbMATH Open document ID: 1028.58011
DOI: 10.1016/S0393-0440(02)00117-1
author: Jialing Dai
author: Doug Pickrell
published in: Journal of Geometry and Physics
publication date: 2003-03-23T00:00:00Z
review text: The paper concerns the orbit method, as it applies to the universal central extension \(\widetilde D\), of \(D=\text{Diff}^+(S^1)\). One reviews the Kirillov-Segal classification of the smooth coadjoint orbits, the boundedness properties of the natural height function and the structure theory for the Virasoro algebra [see \textit{A. A. Kirillov}, Bull. Am. Math. Soc., New Ser. 36, 433--488 (1999; Zbl 0940.22013)] and develops a discussion about the orbital integrals. Expressed in terms of the power series they can suggest some link with supersymmetry. The formulae can be applied to obtain a weak form of asymptotic invariante for Malliavin-Shavgulidze measures.
reviewed by: Maido Rahula
Mathematics Subject Classification ID: 58D20
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 22E67
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 58D05
zbMATH DE Number: 1886807
zbMATH Keywords: orbit methods
zbMATH Keywords: Virasoro extension
zbMATH Keywords: orbital integrals
MaRDI profile type: Publication
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full work available at URL: s0393-0440(02)00117-1
OpenAlex ID: W1619942397
description: scientific article; zbMATH DE number 1886807