Matrix product formula for Uq(A2(1))-zero range process

The U-q(A(n)((1)))-zero range processes introduced recently by Mangazeev, Maruyama and the authors are integrable discrete and continuous time Markov processes associated with the stochastic R matrix derived from the well-known U-q(A(n)((1))) quantum R matrix. By constructing a representation of the relevant Zamolodchikov-Faddeev algebra, we present, for n = 2, a matrix product formula for the steady state probabilities in terms of q-boson operators.