Reaction-diffusion processes as physical realizations of Hecke algebras

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions can be written as a euclideen Schr\"odinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest-neighbour interactions. Since many one-dimensional chains are integrable, this opens a new field of applications. For many reactions the Hamiltonian can be written as the sum of generators of various quotients of the Hecke algebra giving hermitian and non-hermitian (for irreversible processes) representations.