On the Irreducibility of Perron Representations of Degrees 4 and 5
DOI:
https://doi.org/10.29020/nybg.ejpam.v11i1.3199Keywords:
Artin representation, braid group, Burau representation, graph, irreducibilityAbstract
We consider the graph $E_{n+1,1}$ with (n+1) generators $\sigma_1,..., \sigma_{n}$, and $\delta$, where $\sigma_{i}$ has an edge with $\sigma_{i+1}$ for $i=1,...,n+1$, and $
\sigma_{1}$ has an edge with $\delta$. We then define the Artin group of the graph $E_{n+1,1}$ for $n=3$ and $n=4$ and consider its reduced Perron's representation of degrees
four and five respectively. After we specialize the indeterminates used in defining the representation to non-zero complex numbers, we obtain necessary and sufficient
conditions that guarantee the irreducibility of the representations for $n=3$ and $4$ .
Downloads
Published
Issue
Section
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.