On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation

Details On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation

1997-10-02

arxiv.org/abs/solv-int/9709013v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, LaTeX. The references are defined more precisely

Scientific paper

A sort of two dimensional linear auxiliary problem for the complex of 3D $R$ -- operators associated with the Zamolodchikov -- Bazhanov -- Baxter statistical model is proposed. This problem resembles the problem of the local Yang -- Baxter equation but does not coincide with it. The formulation of the auxiliary problem admits a notion of a ``fusion'', and usual local Yang -- Baxter equation appears among other results of this ``fusion''.

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