Kontsevichʹs integral for the Homfly polynomial and relations between values of multiple zeta functions

Kontsevichʹs integral for the Homfly polynomial is studied by using representations of the chord diagram algebras via classical r-matrices for slN and via a Kauffman type state model. We compute the actual value of the image of W(γ) by these representations, where γ is the normalization factor to construct an invariant from the integral. This formula implies relations between values of multiple zeta functions.