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

Abdulrahim, Mohammad

doi:10.1090/S0002-9939-97-04081-1

Complex specializations of the reduced Gassner representation of the pure braid group
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by Mohammad N. Abdulrahim PDF

Proc. Amer. Math. Soc. 125 (1997), 1617-1624 Request permission

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

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