We establish a general 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 SL₃ and SO₅, which is obtained via folding the Dynkin diagram of A₃ into one of B₂.

我们通过使用 Zamolodchikov 四面体方程的已知解，建立了获得 3D 反射方程的集合论解的通用方法，其中前一个方程是由 Isaev 和 Kulish 提出的，作为后者的边界模拟。通过将我们的方法应用于 Sergeev 的电解和与离散修正 KP 方程相关的双分量解，我们获得了 3D 反射方程的新解。我们的方法与S L ₃和S O ₅的全正部分的 Lusztig 参数化的转换图之间的关系密切相关，这是通过将A ₃的 Dynkin 图折叠成B ₂之一而获得的.