Finite conformal modules over the N=2,3,4 superconformal algebras

Abstract

In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated in q-alg/9706030. 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.

36 pages, no figures, LaTeX format

References in corpus (1)

• Formal distribution algebras and conformal algebras

Cited by in corpus (14)

• Representations of simple finite Lie conformal superalgebras of type W and S
• Classification of finite irreducible modules over the Lie conformal superalgebra CK6
• Non-weight modules over the affine-Virasoro algebra of type $A_1$
• Irreducible modules over finite simple Lie conformal superalgebras of type K
• Representations of the affine-Virasoro algebra of type $A_1$
• Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras
• Finite irreducible conformal modules over the Lie conformal superalgebra $\mathcal{S}(p)$
• Classification of finite irreducible conformal modules for $K_4^{\prime }$
• An upper bound on the degree of singular vectors for $E(1,6)$
• Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra
• Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$
• Computation of the homology of the complexes of finite Verma modules for $K_4^{\prime }$
• Universally defined representations of Lie conformal superalgebras
• Classification of simple differential Lie and Jordan (super)coalgebras of finite rank