A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of U_q(A_n^(1))

Atsuo Kuniba, Masato Okado

Luigi Accardi, T. Hida, Win Win Htay

Un Cig Ji

Atsuo Kuniba, Masato Okado

Abstract 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.

Atsuo Kuniba, Masato Okado, Satoshi W. Watanabe

We present a brief review on integrability of multispecies zero range process in one dimension introduced recently.The topics range over stochastic R matrices of quantum affine algebra U q A (1) n , matrix product construction of stationary states for periodic systems, q-boson representation of Zamolodchikov-Faddeev algebra, etc.We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of R matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter.

Franco Fagnola, Carlos Mora