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This article is cited in 1 scientific paper (total in 1 paper)
Integrable Structure of Multispecies Zero Range Process
Atsuo Kunibaa, Masato Okadob, Satoshi Watanabea a Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
b Department of Mathematics, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
Abstract:
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 $U_q\big(A^{(1)}_n\big)$, 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.
Keywords:
integrable zero range process; stochastic $R$ matrix; matrix product formula.
Received: January 26, 2017; in final form June 7, 2017; Published online June 17, 2017
Citation:
Atsuo Kuniba, Masato Okado, Satoshi Watanabe, “Integrable Structure of Multispecies Zero Range Process”, SIGMA, 13 (2017), 044, 29 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1244 https://www.mathnet.ru/eng/sigma/v13/p44
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