Unitary Representations of W Infinity Algebras

We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of W infinity algebras (W∞, W1+∞, W 1,1 ∞ , W M ∞ , W N 1+∞, W M,N ∞ ) with central charges (2, 1, 3, 2M , N , 2M +N). The characters of these representations are computed. We construct a new extended superalgebra W ∞ , whose bosonic sector is W ∞ ⊕ W N 1+∞. 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 . ∗e-mail address: [email protected].