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Using the Fourier expansion of Markov traces for Ariki–Koike algebras over ℚ(q, u1, …, ue), 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 a 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.

WEIGHTS OF MARKOV TRACES OF ALEXANDER POLYNOMIALS FOR MIXED LINKS