Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-07-20
Physics
High Energy Physics
High Energy Physics - Theory
5 pages, LaTex, to be published in Dynamics of Continuous, Discrete and Impulsive Systems-Series A (Special Issue) in 2007
Scientific paper
The superalgebra $\hat{K}'(4)$ and the exceptional N = 6 superconformal algebra 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 these superalgebras into the Lie superalgebras of pseudodifferential symbols on the supercircle S^{1|N}. In this work we describe $\hat{K}'(4)$ and the exceptional N = 6 superconformal algebra in terms of matrices over a Weyl algebra. Correspondingly, we obtain realizations of their representations in $V^{\mu}$ for $\mu = 0$.
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