Symmetry, Integrable Chain Models and Stochastic Processes

Details Symmetry, Integrable Chain Models and Stochastic Processes Symmetry, Integrable Chain Models and Stochastic Processes

1996-05-18

arxiv.org/abs/hep-th/9605130v1

Rev.Math.Phys. 10 (1998) 723-750

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, Latex

Scientific paper

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 models with $A_n$ symmetry and the related Temperley-Lieb algebraic structures and representations are discussed. It is shown that corresponding to these $A_n$ symmetric integrable chain models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains whose spectra of the transition matrices (resp. intensity matrices) are the same as the ones of the corresponding integrable models.

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