Abstract
In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated by Cheng and Kac [Asian J. Math. 1, 181–193 (1997); 2, 153–156 (1998) (erratum)]. We study finite Verma-type conformal modules over the N=2, N=3 and the two N=4 superconformal algebras and also find explicitly all singular vectors in these modules. From our analysis of these modules we obtain a complete list of finite irreducible conformal modules over the N=2, N=3 and the two N=4 superconformal algebras.
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