We study solutions of the reflection equation related to the quantum affine algebra Uq(sln^) . First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct upper- and lower-triangular solutions of the reflection equation related to symmetric tensor representations of Uq(sln^) with arbitrary spin. We also prove the star–star relation for the Boltzmann weights of the Ising-type model, conjectured by Bazhanov and Sergeev, and use it to verify certain properties of the solutions obtained.