Construction of Irreducible Representations of the Quantum Super Group $GL_q(3|1)$

TL;DR

This paper constructs all irreducible representations of the quantum supergroup $GL_q(3|1)$ using the double Koszul complex, advancing the understanding of quantum supergroup representations.

Contribution

It provides a complete construction of irreducible representations of $GL_q(3|1)$, a significant step in quantum supergroup representation theory.

Findings

All irreducible representations of $GL_q(3|1)$ are explicitly constructed.

The double Koszul complex is effectively used for representation construction.

The work enhances the understanding of quantum supergroup structures.

Abstract

In this note, we construct all irreducible representations of the quantum general linear super group $GL_q(3|1)$ using the double Koszul complex.