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Virasoro algebra and Teichmüller spaces. (English. Russian original) Zbl 0647.58012

Funct. Anal. Appl. 21, No. 1-3, 156-157 (1987); translation from Funkts. Anal. Prilozh. 21, No. 2, 78-79 (1987).
It is shown that the set of equivalence classes of triples \((C,p,t)\), where \(C\) is a complex Riemann surface of genus \(g\), \(p\) a point of \(C\) and \(t\) an \(\infty\)-jet of a coordinate at \(p\) is infinitesimally a double coset space of the central extension of the group of diffeomorphisms of the circle (the Virasoro group) modulo analogues of a compact and a discrete subgroup and its embedding into an infinite dimensional Grassmannian is described.
Fortunately, these results, discovered independently, are presented in more detailed and easier to read form in A. A. Beilinson and V. V. Schechtman [Commun. Math. Phys. 118, 651–701 (1988; Zbl 0665.17010)], B. Arbarello, C. De Concini, V. Kac and C. Procesi, Commun. Math. Phys. 117, No. 1, 1–36 (1988; Zbl 0647.17010)] and [N. Kawamoto, Y. Namikawa, A. Tsuchiya and Y. Yamada, Commun. Math. Phys. 116, No. 2, 247–308 (1988; Zbl 0648.35080)].
Reviewer: D.A.Leites

MSC:

58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
17B68 Virasoro and related algebras
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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[1] Yu. I. Manin, Funkts. Anal. Prilozhen.,20, No. 3, 88-89 (1986).
[2] I. V. Cherednik, Funkts. Anal. Prilozhen.,19, No. 3, 36-52 (1985).
[3] D. Mumford, L’Enseign Math., Ser. 2,23, No. 1-2, 39-110 (1977).
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