On representations of the exceptional superconformal algebra $CK_6$

Abstract

We realize the exceptional superconformal algebra $CK_6$, spanned by 32 fields, inside the Lie superalgebra of pseudodifferential symbols on the supercircle $S^{1|3}$. We obtain a one-parameter family of irreducible representations of $CK_6$ in a superspace spanned by 8 fields.