Quantum Dynamical $\check{R}$- Matrix with Spectral Parameter from Fusion

TL;DR

This paper constructs a quantum dynamical R-matrix with spectral parameter using fusion, linking it to the Lie algebra so(3) and highlighting its non-translation-invariant property.

Contribution

It introduces a new spin-1 quantum dynamical R-matrix derived via fusion, expanding the understanding of R-matrices related to so(3).

Findings

Constructed a spectral parameter-dependent R-matrix via fusion.

Connected the R-matrix to the Lie algebra so(3).

Identified the R-matrix as non-translation-invariant.

Abstract

A quantum dynamical $\check{R}$-matrix with spectral parameter is constructed by fusion procedure. This spin-1 $\check{R}$-matrix is connected with Lie algebra $so(3)$ and does not satisfy the condition of translation invariance.