Distance-regular graphs which support a spin model are thin
A spin model \(W\) is a square matrix satisfying certain conditions which ensure that it yields an invariant of knots and links. \textit{F. Jaeger} [Adv. Stud. Pure Math. 24, 197-225 (1996; Zbl 0864.05089)] proved that every symmetric spin model is contained in the Bose-Mesner algebra of some association scheme. In [\textit{K. Nomura}, J. Algebr. Comb. 6, No. 1, 53-58 (1997; Zbl 0865.05077)] a canonical construction \(N(W)\) was given for a Bose-Mesner algebra which contains a given spin model \(W\). In the present paper it is shown that in the case when \(N(W)\) contains a Bose-Mesner algebra of a distance-regular graph \(\Gamma\), the Terwilliger algebra (see Zbl 0785.05089, Zbl 0785.05090, and Zbl 0785.05091) of \(\Gamma\) is thin.
scientific article; zbMATH DE number 1322013