Quantum Group $U_q(sl(2))$ Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain

We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric $R$-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete $2s$-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.