Central elements of the degenerate quantum general linear group

TL;DR

This paper constructs central elements, including a quantum Casimir, for the degenerate quantum general linear group using explicit L operators and the FRT approach, advancing the understanding of its algebraic structure.

Contribution

It provides explicit formulas for central elements and a universal L operator, introducing a spectral parameter-dependent solution to the quantum Yang-Baxter equation.

Findings

Explicit quantum Casimir element derived

Universal L operator constructed with spectral parameter

FRT approach applied to degenerate quantum GL group

Abstract

We construct central elements of the degenerate quantum general linear group introduced by Cheng, Wang and Zhang. In particular, we give an explicit formula for the quantum Casimir element. Our method is based on the explicit $L$ operators. Moreover, we construct a universal $L$ operator, which is a spectral parameter-dependent solution of the quantum Yang-Baxter equation in the tensor product of the degenerate quantum general linear group and the endomorphism ring of its natural representation. This construction leads to the FRT approach to the degenerate quantum general linear group.