Necessary and sufficient conditions for the irreducibility of a linear representation of the braid group $B_n$

IF 0.9 Q2 MATHEMATICS Arabian Journal of Mathematics Pub Date : 2024-07-17 DOI:10.1007/s40065-024-00468-x

Mohamad N. Nasser

引用次数: 0

Abstract

Valerij G. Bardakov and P. Bellingeri introduced a new linear representation $\bar{\rho }_F$ of degree $n+1$ of the braid group $B_n$. We study the irreducibility of this representation. We prove that $\bar{\rho }_F$ is reducible to the degree $n-1$. Moreover, we give necessary and sufficient conditions for the irreducibility of the complex specialization of its $n-1$ degree composition factor $\bar{\phi }_F$.

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辫状群 $$B_n$ 线性表示不可还原性的必要条件和充分条件

巴达科夫（Valerij G. Bardakov）和贝林格里（P. Bellingeri）介绍了辫子群$B_n$的度数为$n+1$的新线性表示$\bar{rho }_F$。我们研究了这个表示的不可还原性。我们证明了 $\bar{\rho }_F$ 是可以还原为度 $n-1/)的。此外，我们还给出了其\(n-1$度组成因子$\bar{\phi }_F$的复特殊化的不可还原性的必要条件和充分条件。

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

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.

Necessary and sufficient conditions for the irreducibility of a linear representation of the braid group \(B_n\)

Abstract