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arXiv · hep-th/9308153

Quasifinite highest weight modules over the Lie algebra of differential operators on the circle

Victor G. Kac·A. Radul
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Abstract

We classify positive energy representations with finite degeneracies of the Lie algebra $W_{1+\infty}\/$ and construct them in terms of representation theory of the Lie algebra $\hatgl ( \infty R_m )\/$ of infinite matrices with finite number of non-zero diagonals over the algebra $R_m = \C [ t ] / ( t^{m + 1} )\/$. The unitary ones are classified as well. Similar results are obtained for the sin-algebras.

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Victor G. Kac, A. Radul. 1993-08-31. Quasifinite highest weight modules over the Lie algebra of differential operators on the circle. https://doi.org/10.1007/bf02096878

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