In this paper, we first give a diagrammatic analogue of the Young symmetrizer. By using this, the (
sl (
N,
C),ρ)-weight system for an arbitrary finite-dimensional irreducible representation ρ is formulated in a diagrammatic way. The formula is useful for the calculations of the (
sl (
N,
C),ρ)-weight system in the sense that we do not need actual constructions of the representations of
sl (
N,
C) essentially. Hence by using this and the modified Kontsevich integral we can get the quantum (
sl (
N,
C),ρ)-invariant for any finite-dimensional irreducible representation without actual constructions of the representations of
sl (
N,
C). The diagrammatic construction is a generalization of the formula given in “Remarks on the (
sl (
N,
C),
ad )-weight system”.
View full abstract