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Triangular solutions to the reflection equation for $U_q(\widehat{sl_n})$

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arxiv 2402.05442 v3 pith:3MCJWJUY submitted 2024-02-08 math-ph cond-mat.stat-mechmath.MPmath.QA

Dmitry Kolyaskin , Vladimir V Mangazeev This is my paper · ORCID
classification math-phcond-mat.stat-mechmath.MPmath.QA
keywords solutionsequationreflectionwidehatconstructrelatedaffinealgebra
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abstract

We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. 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 $U_q(\widehat{sl_n})$ 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.

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  1. The boundary-driven multispecies harmonic process

    math-ph 2026-07 conditional novelty 6.0 of 10

    A multispecies harmonic process with boundary reservoirs is introduced and proven Yang-Baxter integrable via a factorized R-matrix and open-chain K-matrices, with three dual processes.

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