The Lawrence–Krammer representation is a quantization of the symmetric square of the Burau representation

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-08-20 DOI:10.1016/j.laa.2025.08.009

Alexandr V. Kosyak

引用次数: 0

Abstract

We show that the Lawrence–Krammer representation is a quantization of the symmetric square of the Burau representation. Here, by quantization we mean changing the natural numbers by q-natural numbers and the corresponding quantization of the Pascal triangle, appearing naturally in representations of the braid groups. This connection allows us to construct new representations of the braid groups.

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Lawrence-Krammer表示是Burau表示的对称平方的量子化

我们证明了Lawrence-Krammer表示是Burau表示的对称平方的量子化。这里，通过量化，我们指的是用q-自然数改变自然数，以及帕斯卡三角形的相应量化，自然地出现在辫群的表示中。这种连接允许我们构建编织组的新表示。

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.