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Complex specializations of the reduced Gassner representation of the pure braid group

Author: Mohammad N. Abdulrahim
Journal: Proc. Amer. Math. Soc. 125 (1997), 1617-1624
MSC (1991): Primary 20F36
MathSciNet review: 1422839
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Abstract: We will give a necessary and sufficient condition for the specialization of the reduced Gassner representation $G_{n}(z): P_{n} \to GL_{n-1}(\mathbb {C})$ to be irreducible. It will be shown that for $z=(z_{1},\ldots ,z_{n})\in (\mathbb {C}^{*})^{n}$, $G_{n}(z)$ is irreducible if and only if $z_{1}\ldots z_{n} \neq 1$.

References [Enhancements On Off] (What's this?)

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Additional Information

Mohammad N. Abdulrahim
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Keywords: Braid group, pure braid group, Burau representation, Gassner representation
Received by editor(s): December 23, 1995
Additional Notes: The results in this paper were written under the direction of Professor Edward Formanek whose help and encouragement are greatly appreciated.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society