Weights of Markov traces for Alexander polynomials of mixed links

Details Weights of Markov traces for Alexander polynomials of mixed links Weights of Markov traces for Alexander polynomials of mixed links

2011-12-11

arxiv.org/abs/1112.2335v1

Mathematics

Representation Theory

25 pages, 12 figures

Scientific paper

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.

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