Abstract.
We prove that chromatic weight systems, introduced by Chmutov, Duzhin and Lando, can be expressed in terms of weight systems associated with direct sums of the Lie algebras \({\mathfrak{gl}}_n\) and \({\mathfrak{so}}_n\). As a consequence the Vassiliev invariants of knots corresponding to the chromatic weight systems distinguish exactly the same knots as a one-variable specialization \(\Upsilon\) of the Homfly and Kauffman polynomial.
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Received: 22 December 1997 / Revised: 18 March 1999 / Published online: 8 May 2000
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Lieberum, J. Chromatic weight systems and the corresponding knot invariants. Math Ann 317, 459–482 (2000). https://doi.org/10.1007/PL00004409
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DOI: https://doi.org/10.1007/PL00004409