Publications

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 .