Abdulrahim, Mohammad N.; Tarraf, Hassan A. Higher dimensional irreducible representations of the pure braid group. (English) Zbl 1267.20055 J. Math. Res. 3, No. 4, 141-151 (2011). Summary: The reduced Gassner representation is a multi-parameter representation of \(P_n\), the pure braid group on \(n\) strings. Specializing the parameters \(t_1,t_2,\dots,t_n\) to nonzero complex numbers \(x_1,x_2,\dots,x_n\) gives a representation \(G_n(x_1,\dots,x_n)\colon P_n\to\mathrm{GL}(\mathbb C^{n-1})\) which is irreducible if and only if \(x_1\cdots x_n\neq 1\). In a previous work, we found a sufficient condition for the irreducibility of the tensor product of two irreducible Gassner representations. In our current work, we find a sufficient condition that guarantees the irreducibility of the tensor product of three Gassner representations. Next, a generalization of our result is given by considering the irreducibility of the tensor product of \(k\) representations (\(k\geq 3\)). MSC: 20F36 Braid groups; Artin groups 20C15 Ordinary representations and characters Keywords:pure braid groups; Gassner representation; tensor products; irreducibility PDFBibTeX XMLCite \textit{M. N. Abdulrahim} and \textit{H. A. Tarraf}, J. Math. Res. 3, No. 4, 141--151 (2011; Zbl 1267.20055) Full Text: DOI Link