Triangular solutions to the reflection equation for Uq(slₙ)

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.