Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras

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. Permanent adress: Departamento de F́ısica, Universidade Federal de São Carlos, 13560 São Carlos SP, Brasil It is well known in the literature that several integrable quantum chains corresponding to magnetic systems [1] can be represented as generators of Hecke algebras Hn(q), when certain artificial interactions are added in the bulk and the surface. In this letter we show that the master equation describing the dynamics of some chemical processes limited by diffusion give representations of Hecke algebras, where the supplementary interactions appear naturally. The Hecke algebraHn(q) (with n = L−1) is an associative algebra with generators ei (i = 1, . . . , L− 1) satisfying the relations eiei±1ei − ei = ei±1eiei±1 − ei±1 (1) [ei, ej ] = 0 ; |i− j| ≥ 2 (2) ei = (