Triangular solutions to the reflection equation for U q(sl̂n)

Abstract

Abstract We study solutions of the reflection equation related to the quantum affine algebra Uq(sl̂n). 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 the symmetric tensor representations of Uq(sl̂n) 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 obtained solutions.