Diagrammatic construction of an irreducible basis of algebraic invariants for the sixteen vertex model

According to a fundamental theorem by Hilbert the partition function and other physically relevant properties of the general sixteen vertex model must be expressible algebraically in terms of a small number of basic invariants with respect to the symmetry group of the model. The construction of such an irreducible set of algebraic invariants has been described in two earlier papers by Graff and Hijmans1,2). In the present paper it is shown that this basic set can be obtained in a simpler and more elegant way by means of a diagrammatic technique, based on scalar and vectorial multiplication of three kinds of construction elements and the use of six reduction rules for diagrams.