Generalized spin models and association schemes.

Abstract

The concept of spin model was defined by V. F. R. Jones. Recently, F. Jaeger discovered that Bose-Mesner algebras of association schemes are natural places to look for spin models. The purpose of this paper is to study connections between (generalized) generalized spin models and (not necessarily symmetric) association schemes. For arbitrary generalized generalized spin models, we can prove somewhat weaker versions of Jaeger's results. However, we prove the corresponding results of Jaeger in full strength for generalized spin models of Jones type.