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arXiv · 1602.04574

Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation

Atsuo Kuniba·Shouya Maruyama·Masato Okado
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Abstract

We consider a three-dimensional (3D) lattice model associated with the intertwiner of the quantized coordinate ring $A_q(sl_3)$, and introduce a family of layer to layer transfer matrices on $m\times n$ square lattice. By using the tetrahedron equation we derive their commutativity and bilinear relations mixing various boundary conditions. At $q=0$ and $m=n$, they lead to a new proof of the steady state probability of the $n$-species totally asymmetric zero range process obtained recently by the authors, revealing the 3D integrability in the matrix product construction.

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Atsuo Kuniba, Shouya Maruyama, Masato Okado. 2016-02-15. Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation. https://arxiv.org/abs/1602.04574

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