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

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.

References in corpus (1)

• Poisson-Lie group of pseudodifferential symbols and fractional KP-KdV hierarchies

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