Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz

TL;DR

This paper solves matrix difference equations related to the supersymmetric Lie algebra sl(2,1) using a generalized nested algebraic Bethe ansatz, revealing highest-weight solutions within the graded algebra structure.

Contribution

It introduces a novel approach to solving supersymmetric matrix difference equations via a generalized algebraic Bethe ansatz method.

Findings

Solutions are of highest-weight type

Method generalizes nested algebraic Bethe ansatz

Applicable to supersymmetric Lie algebra sl(2,1)

Abstract

Based on the rational R-matrix of the supersymmetric sl(2,1) matrix difference equations are solved by means of a generalization of the nested algebraic Bethe ansatz. These solutions are shown to be of highest-weight with respect to the underlying graded Lie algebra structure.