Chromatic weight systems and the corresponding knot invariants

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.