Integrable boundaries for the q-Hahn process

Taking inspiration from the harmonic process with reservoirs introduced by Frassek, Giardinà and Kurchan in (2020 J. Stat. Phys. 180 135-71), we propose integrable boundary conditions for its trigonometric deformation, which is known as the q-Hahn process. Following the formalism established by Mangazeev and Lu in (2019 Nucl. Phys. B 945 114665) using the stochastic R-matrix, we argue that the proposed boundary conditions can be derived from a transfer matrix constructed in the framework of Sklyanin’s extension of the quantum inverse scattering method and consequently preserve the integrable structure of the model. The approach avoids the explicit construction of the K-matrix.