Classification of degenerate Verma modules over $E(4,4)$

TL;DR

This paper classifies degenerate Verma modules over the Lie superalgebra E(4,4), completing the understanding of Verma modules over exceptional linearly compact Lie superalgebras, and explores their complex structures.

Contribution

It provides the first complete classification of degenerate Verma modules over E(4,4), extending the theory to an exceptional superalgebra.

Findings

Classification of all degenerate Verma modules over E(4,4)

Construction of infinite bilateral complexes from these modules

Generalization of de Rham complexes in this context

Abstract

In this paper we classify degenerate Verma modules over the linearly compact Lie superalgebra $E(4,4)$. This completes the description of Verma modules over the exceptional linearly compact Lie superalgebras. As in the other cases all degenerate modules and morphisms between them give rise to infinite bilateral complexes which may be viewed as a generalization of de Rham complexes.