Double Koszul Complex and Construction of Irreducible Representations of $\frak{gl}(3|1)$

TL;DR

This paper introduces a combinatorial approach to explicitly construct all irreducible representations of the Lie superalgebra rak{gl}(3|1) when the super-dimension of the vector space is (3|1).

Contribution

It provides a novel combinatorial method for describing irreducible representations of rak{gl}(3|1), filling a gap in the explicit construction of these representations.

Findings

Developed a combinatorial framework for rak{gl}(3|1) representations.

Explicitly constructed all irreducible representations in the (3|1) case.

Enhanced understanding of superalgebra representation theory.

Abstract

The aim of this work is to give a combinatorial way to describe all irreducible representations in case the super-dimension of $V$ is $(3|1)$.