TY - JOUR

T1 - Solution of tetrahedron equation and cluster algebras

AU - Gavrylenko, P.

AU - Semenyakin, M.

AU - Zenkevich, Y.

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

KW - Integrable Hierarchies

KW - Lattice Integrable Models

KW - Quantum Groups

UR - http://www.scopus.com/inward/record.url?scp=85105804159&partnerID=8YFLogxK

U2 - 10.1007/JHEP05(2021)103

DO - 10.1007/JHEP05(2021)103

M3 - Article

AN - SCOPUS:85105804159

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 5

M1 - 103

ER -