On the irreducibility of linear representations of the pure braid group

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Mohammad N. Abdulrahim

Abstract

Following up on our result in [1], we find a milder sufficient condition for the tensor product of specializations of the reduced Gassner representation of the pure braid group to be irreducible. We prove that $G_n(x_1, \ldots, x_n) \otimes G_n(y_1, \ldots, y_n) : P_n \to GL(\mathbb{C}^{n-1} \otimes \mathbb{C}^{n-1})$ is irreducible if  $x_i \neq \pm y_i $ and $x_j \neq \pm {{y_j}^{-1}} $ for some $i$ and $j$.

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How to Cite
Abdulrahim, M. N. (2010). On the irreducibility of linear representations of the pure braid group. Tamkang Journal of Mathematics, 41(3), 283–292. https://doi.org/10.5556/j.tkjm.41.2010.727
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Papers
Author Biography

Mohammad N. Abdulrahim

Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon.

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