Homogeneity of a distance-regular graph which supports a spin model

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机构：
[1] Curtin, Brian
[2] Nomura, Kazumasa
来源：
Curtin, B. (curtin@math.usf.edu) | 1600年 / Kluwer Academic Publishers卷 / 19期
关键词：
Algebra - Integer programming - Matrix algebra - Set theory - Statistical mechanics - Theorem proving;
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摘要：
A spin model is a square matrix that encodes the basic data for a statistical mechanical construction of link invariants due to V.F.R. Jones. Every spin model W is contained in a canonical Bose-Mesner algebra N (W). In this paper we study the distance-regular graphs Γ whose Bose-Mesner algebra M satisfies W ∈ M ⊆ N (W). Suppose W has at least three distinct entries. We show that Γ is 1-homogeneous and that the first and the last subconstituents of r are strongly regular and distance-regular, respectively.
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