On the twisted Alexander polynomial for metabelian representations into

We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL 2 ( 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 sl 2 ( C ) , in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.