A state model for the multi-variable Alexander polynomial (Q1314919)

A vertex type state model in \textit{V. G. Turaev's} sense [Invent. Math. 92, No. 3, 527-553 (1988; Zbl 0648.57003)] for the multi-variable (non- reduced) Alexander polynomial is constructed. This model is a colored version of the 6-vertex free-fermion model. Colored braid groups and their Magnus representations are introduced to show the correspondence between the model and the Alexander polynomial. By using this model, the author proposes a new set of axioms for the multi-variable Alexander polynomial.