Abstract

We classify positive energy representations with finite degeneracies of the Lie algebraW 1+∞ and construct them in terms of representation theory of the Lie algebra $$\hat gl(\infty ,R_m )$$ of infinites matrices with finite number of non-zero diagonals over the algebraR 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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