A Diagrammatic Construction of the (sl(N,C),ρ)-Weight System

Abstract

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”.