Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions

We consider the integrable XXZ model with special open boundary conditions that renders its Hamiltonian SU(2)q symmetric, and the one-dimensional quantum Ising model with four different boundary conditions. We show that for each boundary condition the Ising quantum chain is given exactly by the minimal model of integrable lattice theory LM(3,4). This theory is obtained as the result of the quantum group reduction of the XXZ model at anisotropy Δ = (q + q-1)/2 = (2)1/2/2, with a number of sites that depends on the type of imposed boundary condition.