可逆Jones对上的Bose-Mesner代数
Bose-Mesner Algebras attached to Invertible Jones Pairs
摘要：
1989年，沃恩·琼斯引入了自旋模型，并表明它们可以通过两种不同的方式来形成链接不变量-通过构造辫群的表示，或者通过构造分拆函数。这些自旋模型随后被Bannai和Bannai推广为所谓的4权自旋模型;这些模型可以用来构造分拆函数，但没有以任何明显的方式导致辫群表示。耶格指出，自旋模型与某些缔合方案密切相关。Yamada从$n$顶点上的4权自旋模型出发，构造了$4n$顶点上的对称自旋模型.在本文中，我们建立在最近的工作与宗正给山田的结果不同的证明，我们分析了结构的关联方案附加到这个自旋模型。
英文摘要：
In 1989, Vaughan Jones introduced spin models and showed that they could be used to form link invariants in two different ways--by constructing representations of the braid group, or by constructing partition functions. These spin models were subsequently generalized to so-called 4-weight spin models by Bannai and Bannai; these could be used to construct partition functions, but did not lead to braid group representations in any obvious way. Jaeger showed that spin models were intimately related to certain association schemes. Yamada gave a construction of a symmetric spin model on $4n$ vertices from each 4-weight spin model on $n$ vertices. In this paper we build on recent work with Munemasa to give a different proof to Yamada's result, and we analyse the structure of the association scheme attached to this spin model.
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