Symmetric versus non-symmetric spin models for link invariants
In [Pac. J. Math. 137, No. 2, 311-334 (1989; Zbl 0695.46029)] V. F. R. Jones introduced the notion of a spin model and associated a complex number to it which is a link invariant. A spin model is a triple \((X, w_+, w_-)\) where \(X\) is a finite set and \(w_+\) and \(w_-\) are complex matrices with rows and columns indexed by \(X\). In the definition of Jones these matrices are symmetric. The first author used in [Geom. Dedicata 44, No. 1, 23-52 (1992; Zbl 0773.57005)] association schemes to construct spin models which has led to a generalization to non-symmetric matrices. The link invariants associated to symmetric spin models depend only trivially on the orientation of the link. In this paper non-symmetric Hadamard spin modules are defined which give the first known examples of a non-symmetric spin model where the associated link invariants depend non-trivially on the orientation of the link.
scientific article; zbMATH DE number 1389485