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

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

1993-08-31

arxiv.org/abs/hep-th/9308153v1

Commun.Math.Phys. 157 (1993) 429-457

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/BF02096878

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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