Projectivised representations of $U_q osp(2,2)$

TL;DR

This paper constructs finite difference operator representations of the quantum superalgebra $U_q osp(2,2)$ and explores their relevance to quasi-exactly-solvable equations, advancing algebraic and analytical methods.

Contribution

It introduces a novel finite difference operator representation of $U_q osp(2,2)$ and connects it to quasi-exact solvability, expanding the understanding of quantum superalgebra representations.

Findings

Finite difference operator representations of $U_q osp(2,2)$ are constructed.

The representations are linked to quasi-exactly-solvable equations.

The work provides new tools for algebraic and analytical studies of quantum superalgebras.

Abstract

We construct representations of the enveloping algebra $U_q osp(2,2)$ in terms of finite difference operators and we discuss this result in the framework of quasi-exactly-solvable equations.