On the twisted Alexander polynomial for metabelian representations into SL2(C)SL2(C)

We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL2(C)SL2(C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the twisted Alexander polynomial for irreducible metabelian representations with the adjoint action on sl2(C)sl2(C), in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.