Boundary from Bulk Integrability in Three Dimensions: 3D Reflection Maps from Tetrahedron Maps
Boundary from Bulk Integrability in Three Dimensions: 3D Reflection Maps from Tetrahedron Maps
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DOI：
10.1007/s11040-021-09393-3
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Akihito Yoneyama
中科院分区：
文献类型：
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作者：
Akihito Yoneyama
我们建立了一个通用的方法，通过使用已知的Zamolodchikov四面体方程，其中前一个方程是由Isaev和Kulish提出的边界模拟的三维反射方程的集合理论的解决方案。通过将我们的方法应用到Sergeev的电解和与离散的修正KP方程相关联的双分量解，我们获得了三维反射方程的新解。我们的方法是密切相关的Lusztig的参数化的SL 3和SO 5，这是通过折叠Dynkin图A3到B2之一，得到的完全正的部分之间的过渡映射的关系。
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 ofSL3andSO5, which is obtained via folding the Dynkin diagram ofA3into one ofB2.