Spin models constructed from Hadamard matrices

Abstract

A spin model (for link invariants) is a square matrix $W$ which satisfies certain axioms. For a spin model $W$, it is known that $W^TW^{-1}$ is a permutation matrix, and its order is called the index of $W$. F. Jaeger and K. Nomura found spin models of index 2, by modifying the construction of symmetric spin models from Hadamard matrices. The aim of this paper is to give a construction of spin models of an arbitrary even index from any Hadamard matrix. In particular, we show that our spin models of indices a power of 2 are new.