Random walk invariants of string links from R-matrices (Q258859)

A \textit{string link} is a tangle class \(T:\tau^n\rightarrow \tau^n\) with precisely \(n\) interval components, and a diagram where each interval has one endpoint at the bottom and the other endpoint at the top of the diagram. The authors show that the exterior powers of the matrix valued random walk invariant of string links, introduced by \textit{X.-S. Lin} et al. [Pac. J. Math. 182, No. 2, 289--302 (1998; Zbl 0903.57003)], are isomorphic to the graded components of the tangle functor associated to the Alexander polynomial by \textit{T. Ohtsuki} [Quantum invariants. A study of knots, 3-manifolds, and their sets. Singapore: World Scientific (2002; Zbl 0991.57001)] divided by the zero graded invariant of the functor. Several resulting properties of these representations of the string link monoids are discussed.