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

@article{Kuniba2015MultispeciesTA,
  title={Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation},
  author={Atsuo Kuniba and Shouya Maruyama and Masato Okado},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
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… 

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