A BGG-type resolution for tensor modules over general linear superalgebra

TL;DR

This paper constructs a BGG-type resolution for tensor modules over the general linear superalgebra, providing new insights into their structure and submodules.

Contribution

It introduces a novel BGG-type resolution using Kac modules for finite-dimensional irreducible tensor representations of the superalgebra.

Findings

Resolution expressed as direct sums of Kac modules

Maximal submodule generated by proper singular vector

Enhanced understanding of module structure and submodules

Abstract

We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique maximal submodule of a corresponding reducible Kac module is generated by its proper singular vector.