Finite orbits of the braid group actions

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-11-05 DOI:10.1016/j.geomphys.2024.105363

Jialin Zhang

引用次数: 0

Abstract

We study the finite orbits of the braid group

B_{n}

action on the space of

n \times n

upper-triangular matrices with 1's along the diagonal. On one hand, we give a necessary condition for a matrix M to be in a finite orbit; on the other hand, we classify and provide lengths of finite orbits in low-dimensional matrices and some other important cases. As the finite orbits on

3 \times 3

matrix were crucial to finding the algebraic solutions of the sixth Painlevé equation, we hope the finite orbits on generic

n \times n

matrices to be useful to finding solutions of higher order Painlevé type differential equations.

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辫状群作用的有限轨道

我们研究了对角线上有 1 的 n×n 上三角矩阵空间的辫状群 Bn 作用的有限轨道。一方面，我们给出了矩阵 M 处于有限轨道的必要条件；另一方面，我们对低维矩阵和其他一些重要情况下的有限轨道进行了分类，并给出了有限轨道的长度。正如 3×3 矩阵上的有限轨道对找到第六个潘列维方程的代数解至关重要，我们希望通用 n×n 矩阵上的有限轨道对找到高阶潘列维类型微分方程的解有用。

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

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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