Classification of finite irreducible conformal modules for $K_4^{\prime }$

Abstract

We classify the finite irreducible modules over the conformal superalgebra $K_4^{\prime }$ by their correspondence with finite conformal modules over the associated annihilation superalgebra $\mathcal{A}(K_4^{\prime })$. This is achieved by a complete classification of singular vectors in generalized Verma modules for $\mathcal{A}(K_4^{\prime })$. We also show that morphisms between generalized Verma modules can be arranged in infinitely many bilateral complexes.

52 pages, 1 figure

References in corpus (3)

• Representations of simple finite Lie conformal superalgebras of type W and S
• Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras
• Classification of degenerate Verma modules for E(5,10)

Cited by in corpus (2)

• An upper bound on the degree of singular vectors for $E(1,6)$
• Computation of the homology of the complexes of finite Verma modules for $K_4^{\prime }$