SYMMETRY, INTEGRABLE CHAIN MODELS AND STOCHASTIC-PROCESSES

A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain mod els with A, symmetry and the related Temperley-Lieb algebraic structur es and representations are discussed. It is shown that corresponding t o these A, symmetric integrable chain models there are exactly solvabl e stationary discrete-time (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which co incide with the ones of the corresponding integrable models.