Algebraic properties of twisted Alexander polynomial and Reidemeister torsion of torus knots

In this paper we prove that every coefficient of twisted Alexander polynomials of torus knots associated with irreducible ${\mathrm{S}\mathrm{L}}_n(\mathbb{C})$-representations is an $\mathbb{A}$-valued locally constant function on the ${\mathrm{S}\mathrm{L}}_n(\mathbb{C})$-character variety, where $\mathbb{A}$ is the ring of all algebraic integers over $\mathbb{C}$. Moreover, as a generalization of a recent result of Kitano and Nozaki, we show that ${\mathrm{S}\mathrm{L}}_n(\mathbb{C})$-Reidemeister torsions are algebraic integers for many Seifert fibered spaces. Also, we discuss the power sums of Reidemeister torsions of torus knots for low-dimensional irreducible representations that provide a mysterious relation to TQFT.