Boundary from Bulk Integrability in Three Dimensions: 3D Reflection Maps from Tetrahedron Maps

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2021-06-18 DOI:10.1007/s11040-021-09393-3

Akihito Yoneyama

引用次数: 6

Abstract

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.

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三维体可积性边界:四面体映射的三维反射映射

利用已知的Zamolodchikov四面体方程的集理论解，建立了三维反射方程集理论解的一般方法，其中Zamolodchikov四面体方程是Isaev和Kulish作为后者的边界模拟而提出的。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，我们得到了三维反射方程的新解。我们的方法与SL3和SO5的全正部分的Lusztig参数化转换映射之间的关系密切相关，该转换映射是通过将A3的Dynkin图折叠成B2的Dynkin图而得到的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.