Using the Fourier expansion of Markov traces for Ariki-Koike algebras over $\mathbb{ Q}(q,u_{ 1},...,u_{ e})$, we give a direct definition of the Alexander polynomials for mixed links. We observe that under the corresponding specialization of a Markov parameter, the Fourier coefficients of Markov traces take quite simple form. As a consequence, we show that the Alexander polynomial of a mixed link is essentially equal to the Alexander polynomial of the link obtained by resolving the twisted parts.
Categories: math.RT math.GT math.QA