Symmetry of Reidemeister torsion on SU2-representation spaces of knots

We study two sorts of actions on the space of conjugacy classes of irreducible SU2-representations of a knot group. One of them is an involution which comes from the algebraic structure of SU2 and the other is the action by the outer automorphism group of the knot group. In particular, we consider them on a 1-dimensional smooth part of the space, which is canonically oriented and metrized via a Reidemeister torsion volume form. As an application we show that the Reidemeister torsion function on the 1-dimensional subspace has symmetry about the metrization.