Integrable Lattice Systems and Markov Processes

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 An-symmetric chain models and the SU(2)-invariant ladder models are investigated. It is shown that corresponding to these An-symmetric chain models and SU(2)invariant ladder models there are exactly solvable stationary discretetime (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models. PACS numbers: 02.50.-r, 64.60.Cn, 05.20.-y SFB 256; BiBoS; CERFIM(Locarno); Acc. Arch.; USI(Mendriso) Institute of Applied Mathematics, Chinese Academy of Science, Beijing