# 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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