This paper introduces a polynomial invariant for tame oriented links using representations of the braid group. It begins by discussing Alexander's theorem, which states that any tame oriented link can be represented by a braid. The paper then explains Markov's theorem, which provides a way to determine when two braids represent the same link. Markov moves of two types are defined, and the theorem states that two braids represent the same link if they are equivalent under these moves. However, there is no known algorithm to determine equivalence between two braids. The paper also discusses the Burau representation, a representation of the braid group that has been used to study links. The determinant of the Burau matrix gives the Alexander polynomial of the closed braid, but the normalization of the Alexander polynomial is difficult to predict. The main contribution of this paper is the introduction of a new polynomial invariant for tame oriented links. This invariant is derived from certain representations of the braid group and depends only on the closed braid. The dependence of the invariant on the closed braid is a consequence of Markov's theorem and a trace formula. The trace formula was discovered due to the uniqueness of the trace on certain von Neumann algebras called type II₁ factors. The paper also notes that the Alexander polynomial is normalized to be symmetric in t and t⁻¹ and satisfies Δ(1) = 1, as in Conway's tables.This paper introduces a polynomial invariant for tame oriented links using representations of the braid group. It begins by discussing Alexander's theorem, which states that any tame oriented link can be represented by a braid. The paper then explains Markov's theorem, which provides a way to determine when two braids represent the same link. Markov moves of two types are defined, and the theorem states that two braids represent the same link if they are equivalent under these moves. However, there is no known algorithm to determine equivalence between two braids. The paper also discusses the Burau representation, a representation of the braid group that has been used to study links. The determinant of the Burau matrix gives the Alexander polynomial of the closed braid, but the normalization of the Alexander polynomial is difficult to predict. The main contribution of this paper is the introduction of a new polynomial invariant for tame oriented links. This invariant is derived from certain representations of the braid group and depends only on the closed braid. The dependence of the invariant on the closed braid is a consequence of Markov's theorem and a trace formula. The trace formula was discovered due to the uniqueness of the trace on certain von Neumann algebras called type II₁ factors. The paper also notes that the Alexander polynomial is normalized to be symmetric in t and t⁻¹ and satisfies Δ(1) = 1, as in Conway's tables.