2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123743We provide two methods of producing the $Q$-operator of XXZ spin chain of higher spin, one for $N$th root-of-unity $q$ with odd $N$ and another for a general $q$, as the generalization of those known in the six-vertex model. In the root-of-unity case, we discuss the functional relations involving the constructed $Q$-operator for the symmetry study of the theory. The $Q$-operator of XXZ chain of higher spin for a generic $q$ is constructed by extending Baxter's argument in spin-1/2 case for the six-vertex $Q$-operator.Latex 15 pagesStatistical MechanicsHigh Energy Physics - TheoryMathematical PhysicsQuantum AlgebraExactly Solvable and Integrable Systemstext