FINITE-DIMENSIONAL REPRESENTATIONS OF THE QUADRATIC ALGEBRA - APPLICATIONS TO THE EXCLUSION PROCESS

We study the one-dimensional partially asymmetric simple exclusion pro cess (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida and coworkers showed in 1993 that the stationary pr obability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebr a. We construct all finite-dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density a s well as all correlation lengths for the ASEP on a set of special cur ves of the phase diagram.