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Zbl 0972.81554
Odake, Satoru
Unitary representations of $W$ infinity algebras.
(English)
[J] Int. J. Mod. Phys. A 7, No.25, 6339-6355 (1992). ISSN 0217-751X

Summary: We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of $W$ infinity algebras $(W_\infty, W_{1+\infty}, W_\infty^{1,1}, W_\infty^M, W_{1+\infty}^N, W_\infty^{M,N})$ with central charges $(2, 1, 3, 2M, N, 2M+N)$. The characters of these representations are computed. We contruct a new extended superalgebra $W_\infty^{M,N}$, whose bosonic sector is $W_\infty^M \otimes W_{1+\infty}^N$. Its representations obtained from a free field realization with central charge $2M+N$, are classified into two classes: continuous series and discrete series. For the former there exists a supersymmetry, but for the latter a supersymmetry exists only for $M=N$.
MSC 2000:
*81R10 Repres. of infinite-dim. groups and algebras from quantum theory
17B68 Virasoro and related algebras
81T40 Two-dimensional field theories, etc.

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