Abstract: | |
The ($sl(N,\mathbb{C})$,ad)-weight system is a linear
map from the vector space generated by chord diagrams
to $\mathbb{C}$ associated with simple Lie algebra
$sl(N,\mathbb{C})$ and its adjoint representation ad.
This linear map derives the universality of Kontsevich
invariant to the quantum invariants and Vassiliev
invariants of links.
In this talk, I derive a formula of the ($sl(N,\mathbb{C})$,{\rm ad})-weight system for chord diagram. This is useful for quick calculation of weight system. Furthermore this formula is a generalization of the formulae obtained by Chmutov-Varchenko and Kuga-Yoshizumi in the case of ($sl(2,\mathbb{C})$,ad) |