Triangular solutions to the reflection equation for Uq (sln )

Abstract

We study solutions of the reflection equation related to the quantum affine algebra U-q(sl(n)). 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 U-q(sl(n)) 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. Show more