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Using notation inherited from the six-vertex model, we construct diagramsthat represent the action of the factorizing $F$-matrices associated to thefinite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorizethe tensor $R^{\sigma}_{1... n}$ corresponding with elements of the permutationgroup. We consider in particular the diagram for the tensor $R^{\sigma_c}_{1...n}$, which cyclically permutes the spin chain. This leads us to a diagrammaticconstruction of the local spin operators $S_i^{\pm}$ and $S_i^{z}$ in terms ofthe monodromy matrix operators.

Factorizing $F$-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective