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Quasifinite highest weight modules over the super $W\sb{1+\infty}$ algebra. (English) Zbl 0832.17026
The $W_{1+ \infty}$ algebra is a central extension of the Lie algebra of differential operators on the circle. Such algebras were studied and their quasifinite representations were classified by {\it V. Kac} and {\it A. Radul} [Commun. Math. Phys. 157, 429-457 (1993; Zbl 0826.17027)]. The authors extend these results to the super case. $SW_{1+\infty}$ is a central extension of the Lie super algebra of super differential operators acting on the polynomial algebra over $2\times 2$ super matrices. Again quasifiniteness is characterised by polynomials and the highest weights are expressed in terms of differential equations. As an example a $(B, C)$-system is considered.

17B68Virasoro and related algebras
17B70Graded Lie (super)algebras
81T40Two-dimensional field theories, conformal field theories, etc.
81T60Supersymmetric field theories
Full Text: DOI
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