On constant U_q(sl_2)-invariant R-matrices

TL;DR

This paper investigates constant U_q(sl_2)-invariant R-matrices satisfying the Yang-Baxter equation, revealing that under certain spectral conditions, they are either the Drinfeld R-matrix or its inverse.

Contribution

It characterizes the spectral resolution of U_q(sl_2)-invariant R-matrices and identifies conditions under which they are uniquely determined as the Drinfeld R-matrix or its inverse.

Findings

If the two highest coefficients in the spectral resolution differ, R is either the Drinfeld R-matrix or its inverse.

The spectral resolution provides a criterion for classifying U_q(sl_2)-invariant solutions.

The result narrows down the form of invariant R-matrices under specific spectral conditions.

Abstract

The spectral resolution of a U_q(sl_2)-invariant solution R of the constant Yang-Baxter equation in the braid group form is considered. It is shown that, if the two highest coefficients in this resolution are not equal, then R is either the Drinfeld R-matrix or its inverse.