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

Abstract

We consider a three-dimensional (3D) lattice model associated with the intertwiner of the quantized coordinate ring $A_q(s{l}_3)$, 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.

15 pages, minor corrections

References in corpus (4)

• Multispecies TASEP and the tetrahedron equation
• Multispecies TASEP and combinatorial $R$
• Algebraic construction of multi-species q-Boson system
• Multispecies totally asymmetric zero range process: I. Multiline process and combinatorial $R$

Cited by in corpus (1)

• Multispecies totally asymmetric zero range process: I. Multiline process and combinatorial $R$