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Unitary representations of W infinity algebras. (English) Zbl 0972.81554
Summary: We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of W infinity algebras (W ,W 1+ ,W 1,1 ,W M ,W 1+ N ,W 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 M,N , whose bosonic sector is W M W 1+ 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:
81R10Infinite-dimensional groups and algebras motivated by physics
17B68Virasoro and related algebras
81T40Two-dimensional field theories, conformal field theories, etc.