New Solutions to the Yang--Baxter Equation from Two--Dimensional Representations of $U_q(sl(2))$ at Roots of Unit

TL;DR

This paper introduces new, simple solutions to the Yang--Baxter equation derived from two-dimensional cyclic representations of quantum $SU(2)$ at roots of unity, with applications in scattering matrices and dynamical symmetries.

Contribution

It provides novel solutions to the Yang--Baxter equation using two-dimensional cyclic representations of quantum $SU(2)$ at roots of unity.

Findings

New solutions to the Yang--Baxter equation are constructed.

Solutions can be interpreted as scattering matrices of relativistic objects.

Quantum group acts as a dynamical symmetry in these solutions.

Abstract

We present particularly simple new solutions to the Yang--Baxter equation arising from two--dimensional cyclic representations of quantum $SU(2)$. They are readily interpreted as scattering matrices of relativistic objects, and the quantum group becomes a dynamical symmetry.