Complex specializations of the reduced Gassner representation of the pure braid group期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Mohammad N. Abdulrahim

Affiliation:	Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

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 $z_{1}ldots z_{n} neq 1$ .

Keywords:	Braid group pure braid group Burau representation Gassner representation

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