Homology of the complexes of finite Verma modules over $CK_6$

TL;DR

This paper computes the homology of complexes of finite Verma modules over a specific superalgebra, enabling explicit realization of irreducible quotients of these modules, advancing understanding in conformal superalgebra representation theory.

Contribution

It provides the first explicit homology calculations for complexes of finite Verma modules over the superalgebra (CK_6), revealing their irreducible quotients.

Findings

Homology of the first and third quadrants computed

Explicit realization of irreducible quotients achieved

Enhanced understanding of module structure over (CK_6)

Abstract

We compute the homology of the first and third quadrants of the complexes of finite Verma modules over the annihilation superalgebra $\mathcal{A}(CK_{6})\cong E(1,6)$, associated with the conformal superalgebra $CK_6$, obtained in \cite{ck6}. This computation allows us to explicitly realize the irreducible quotients of degenerate finite Verma modules over $\mathcal{A}(CK_{6})$.