  We show that the master equation governing the dynamics of simple diffusion
and certain chemical reaction processes in one dimension give time evolution
operators (Hamiltonians) which are realizations of Hecke algebras. In the case
of simple diffusion one obtains, after similarity transformations, reducible
hermitian representations while in the other cases they are non-hermitian and
correspond to supersymmetric quotients of Hecke algebras.
