arXiv:2402.05442 · Journal of Physics A Mathematical and Theoretical

Triangular solutions to the reflection equation for U q ( s l n ^ )

Dmitry Kolyaskin, Vladimir V. Mangazeev

Published May 17, 2024• 0 citations

Abstract

Abstract We study solutions of the reflection equation related to the quantum affine algebra U q ( s l 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 ( s l 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.

DOI: 10.1088/1751-8121/ad4d2f

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