We show how Conway's multivariable potential function can be constructed using braids and the reduced Gassner representation. The resulting formula is a multivariable generalization of a construction, due to Kassel-Turaev, of the Alexander-Conway polynomial in terms of the Burau representation. Apart from providing an efficient method of computing the potential function, our result also removes the sign ambiguity in the current formulas which relate the multivariable Alexander polynomial to the reduced Gassner representation. We also relate the distinct definitions of this representation which have appeared in the literature.

中文翻译：

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通过 Gassner 表示的康威势函数

我们展示了如何使用辫子和简化的 Gassner 表示来构建康威的多变量势函数。由于 Kassel-Turaev，得出的公式是根据 Burau 表示的 Alexander-Conway 多项式构造的多变量推广。除了提供计算势函数的有效方法之外，我们的结果还消除了当前公式中的符号歧义，这些公式将多变量亚历山大多项式与简化的 Gassner 表示相关联。我们还涉及文献中出现的这种表示的不同定义。