Kolyaskin, DmitryMangazeev, Vladimir V.2025-06-112025-06-111751-8113WOS:001235793900001ORCID:/0000-0001-6017-9231/work/165895092http://www.scopus.com/inward/record.url?scp=85195056995&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733758570We 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.25enPublisher Copyright: © 2024 The Author(s). Published by IOP Publishing Ltd.Integrable systemsReflection equationStar-star relationStochastic processesYang-Baxter equation2024-06-1410.1088/1751-8121/ad4d2f85195056995