Classification of finite irreducible conformal modules for $K'_4$

TL;DR

This paper classifies finite irreducible modules over the conformal superalgebra $K'_4$ by analyzing singular vectors and morphisms in generalized Verma modules, advancing understanding of their structure.

Contribution

It provides a complete classification of finite irreducible modules over $K'_4$ and explores the structure of morphisms between generalized Verma modules.

Findings

Complete classification of finite irreducible modules for $K'_4$

Identification of singular vectors in generalized Verma modules

Infinite bilateral complexes of morphisms between modules

Abstract

We classify the finite irreducible modules over the conformal superalgebra $K'_{4}$ by their correspondence with finite conformal modules over the associated annihilation superalgebra $\mathcal A(K'_{4})$. This is achieved by a complete classification of singular vectors in generalized Verma modules for $\mathcal A(K'_{4})$. We also show that morphisms between generalized Verma modules can be arranged in infinitely many bilateral complexes.