Spin models of index 2 and Hadamard models

Abstract

A spin model (for link invariants) is a square matrix W with non-zero complex entries which satisfies certain axioms. Recently it was shown that tWW-1 is a permutation matrix (the order of this permutation matrix is called the "index" of W), and a general form was given for spin models of index 2. Moreover, new spin models, called non-symmetric Hadamard models, were constructed. In the present paper, we classify certain spin models of index 2, including non-symmetric Hadamard models.