Integrable Lattice Systems and Markov Processes
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Lattice 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, Latex
30 pages, Latex