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The superalgebra $\hat{K}'(4)$ and the exceptional N = 6 superconformalalgebra have ``small'' irreducible representations in the superspaces $V^{\mu}= t^{\mu}\C[t, t^{-1}]\otimes\Lambda(N)$, where N = 2 and 3, respectively. For${\mu \in \C\backslash \Z}$ they are associated to the embeddings of thesesuperalgebras into the Lie superalgebras of pseudodifferential symbols on thesupercircle S^{1|N}. In this work we describe $\hat{K}'(4)$ and the exceptionalN = 6 superconformal algebra in terms of matrices over a Weyl algebra.Correspondingly, we obtain realizations of their representations in $V^{\mu}$for $\mu = 0$.

On matrix realizations of the contact superconformal algebra $\hat{K}'(4)$ and the exceptional N = 6 superconformal algebra