Matrix product formula for $U_q(A^{(1)}_2)$-zero range process

Atsuo Kuniba; Masato Okado

doi:10.1088/1751-8121/50/4/044001

paper

Matrix product formula for $U_{q} (A_{2}^{(1)})$ -zero range process

arXiv:1608.02779 · doi:10.1088/1751-8121/50/4/044001

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.

15 pages. Section 1 revised

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Abstract

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Matrix product formula for $U_{q} (A_{2}^{(1)})$ -zero range process