Distance-regular graphs which support a spin model are thin
type: Item
instance of: scholarly article
title: Distance-regular graphs which support a spin model are thin
zbMATH Open document ID: 0929.05095
DOI: 10.1016/S0012-365X(99)90065-1
published in: Discrete Mathematics
publication date: 1999-08-09T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1322013
zbMATH Keywords: spin model
zbMATH Keywords: Bose-Mesner algebra
zbMATH Keywords: association scheme
zbMATH Keywords: distance-regular graph
zbMATH Keywords: Terwilliger algebra
author: Brian Curtin
reviewed by: Alexander A. Ivanov
MaRDI profile type: Publication
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full work available at URL: s0012-365x(99)90065-1
OpenAlex ID: W4210532232
description: scientific article; zbMATH DE number 1322013