Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps

DOI10.1007/S11040-021-09393-3arXiv2103.01105MaRDI QIDQ6361840

Publication date: 1 March 2021

Abstract: We established a method for obtaining set-theoretical solutions to the 3D reflection equation by using known ones to the Zamolodchikov tetrahedron equation, where the former equation was proposed by Isaev and Kulish as a boundary analog of the latter. By applying our method to Sergeev's electrical solution and a two-component solution associated with the discrete modified KP equation, we obtain new solutions to the 3D reflection equation. Our approach is closely related to a relation between the transition maps of Lusztig's parametrizations of the totally positive part of

S L_{3}

and

S O_{5}

, which is obtained via folding the Dynkin diagram of

A_{3}

into one of

B_{2}

.

Mathematics Subject Classification ID

Applications of Lie algebras and superalgebras to integrable systems (17B80) Yang-Baxter equations and Rota-Baxter operators (17B38)

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