A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of $$varvec{U_ q(A^{(1)}_n)}$$U q(An(1))

We construct a q-boson representation of the Zamolodchikov-Faddeev algebra whose structure function is given by the stochastic R matrix of (U_q(A^{(1)}_n)) introduced recently. The representation involves quantum dilogarithm type infinite products in the (n(n-1)/2)-fold tensor product of q-bosons. It leads to a matrix product formula of the stationary probabilities in the (U_q(A_n^{(1)}))-zero range process on a one-dimensional periodic lattice.