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Unitary representations of the Virasoro and super-Virasoro algebras. (English) Zbl 0588.17014
Any unitary highest weight representation of the Virasoro algebra is determined by a pair of real numbers (c,h); unitarity implies $c\ge 0$, $h\ge 0$. When $c\ge 1$ it is easy to find a corresponding representation. When $c<1$ it was shown by {\it D. Friedan}, {\it Z. Qiu} and {\it S. Shenker} [Vertex operators in mathematics and physics, Publ., Math. Sci. Res. Inst. 3, 419-449 (1985; Zbl 0559.58010)] that c belongs to an infinite discrete set and for each such c, h can take only a finite number of values. In previous papers the authors developed a method to obtain representations corresponding to some values of $c<1$. In the present paper they show that the method in fact provides all the possible unitary highest weight representations of the Virasoro algebra, thus completing its classification. By a similar method they complete the classification of the unitary highest weight representations of the super-Virasoro algebras.
Reviewer: F.Levstein

17B65Infinite-dimensional Lie (super)algebras
17B10Representations of Lie algebras, algebraic theory
58E05Abstract critical point theory
Full Text: DOI
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