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Quasifinite highest weight modules over the super \(W_{1+\infty}\) 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 V. Kac and 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.

17B68 Virasoro and related algebras
17B70 Graded Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
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