The differential realization of new solutions for Yang-Baxter equation (Q1200694)

Using a \(q\)-differential realization of the quantum algebra \(sl_ q(2)\) on the Bargmann space, which is obtained in comparison to its \(q\)-boson \((q\)-oscillator) realization, we construct the indecomposable representation of \(sl_ q(2)\) for \(q\) a root of unity. Then, we obtain some new solutions for the Yang-Baxter equation \(R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}\) from these new representations. These new solutions are different from both the standard solutions and the non-standard ones.