2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90582Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder models are investigated. It is shown that corresponding to these $A_n$-symmetric chain models and SU(2)-invariant ladder models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.30 pages, LatexQuantum Physicstext