Abstract

This text is a continuation of the overview “Knot polynomials from \(\mathcal{R}\)-matrices: where is physics?” (Phys. Part. Nucl. 51, 172 (2020)). We continue to discuss the basics of a popular subject in modern mathematical physics: describing knots by means of \(\mathcal{R}\)-matrix polynomials. Having discussed the physical context, we now focus on the mathematical apparatus, in which topology, the theory of integrable systems, and the representation theory of quantum groups are intertwined. This text is intended as an introduction to the subject for all those interested in this topic.

中文翻译：

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来自 $$\mathcal{R}$$ 的结多项式 - 矩阵：为什么会出现这个数学？

摘要

本文是概述“来自\(\mathcal{R}\) -matrices 的Knot polynomials : where isphysics?”概述的延续。(Phys. Part. Nucl. 51 , 172 (2020))。我们继续讨论现代数学物理学中一个流行主题的基础知识：通过\(\mathcal{R}\)矩阵多项式描述节点。在讨论了物理环境之后，我们现在关注数学装置，其中拓扑学、可积系统理论和量子群的表示理论交织在一起。本文旨在为所有对此主题感兴趣的人介绍该主题。