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In this paper we show that a variety of interacting particle systems withmultiple species can be viewed as random walks on Hecke algebras. This class ofsystems includes the asymmetric simple exclusion process (ASEP), M-exclusionTASEP, ASEP(q,j), stochastic vertex models, and many others. As an application,we study the asymptotic behavior of second class particles in some of thesesystems.

Interacting particle systems and random walks on Hecke algebras