The orbit method and the Virasoro extension of \(\text{diff}^+(S^1)\). I: Orbital integrals
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.
scientific article; zbMATH DE number 1886807