Solution of tetrahedron equation and cluster algebras

P. Gavrylenko, M. Semenyakin, Y. Zenkevich

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    1 Citation (Scopus)


    We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations. As an application of the new formalism, we show how to construct an integrable system with the spectral curve with arbitrary symmetric Newton polygon. Finally, we embed this integrable system into the double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to the general non-symmetric Newton polygons, and prove the Lemma which classifies conjugacy classes in double affine Weyl groups of A-type by decorated Newton polygons.

    Original languageEnglish
    Article number103
    JournalJournal of High Energy Physics
    Issue number5
    Publication statusPublished - May 2021


    • Integrable Hierarchies
    • Lattice Integrable Models
    • Quantum Groups


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