New constructions of models for link invariants
New constructions of models for link invariants
复制标题
链接不变量模型的新构造
DOI：
10.2140/pjm.1996.176.71
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发表时间：
1996
影响因子：
0.6
通讯作者：
F. Jaeger
中科院分区：
文献类型：
--
作者：
F. Jaeger
我们研究了三种类型的统计力学模型的链接不变量（顶点，IRF和自旋模型）和它们之间的一些关系时，他们表现出一定的对称性所描述的阿贝尔群。特别是我们证明了三种模型的等价性：阿贝尔群X上的强保守顶点模型，同一群X上的双平移不变IRF模型，直积X x X上的平移不变自旋模型.给出了从顶点模型构造自旋模型的一些例子（相关的链接不变量是方向扭曲的生成函数、Jones多项式和Fox着色数）。然后，我们介绍了一个组成的链接不变量的分解成其组件的链接，我们探讨了顶点，IRF和自旋模型之间的上述对应关系与此操作。作为一个主要结果，我们证明了最近由K。从阿达玛矩阵的野村是两个琼斯多项式的合成。
We study three types of statistical mechanical models for link invariants (vertex, IRF and spin models) and some relations between them when they exhibit certain symmetries described by an Abelian group. In particular we show the equivalence of three kinds of models: strongly conservative vertex models on an Abelian group X, doubly translation invariant IRF models on the same group X, and translation invariant spin models on the direct product X x X. Some examples of constructions of spin models from vertex models are given (the associated link invariants are the generating function for the writhe of orientations, the Jones polynomial, and the number of Fox colourings). Then we introduce a composition of link invariants related to the decomposition of a link into its components, and we explore the above correspondence between vertex, IRF and spin models in connection with this operation. As a main consequence, we show that the link invariant associated with spin models recently constructed by K. Nomura from Hadamard matrices is a composition of two Jones polynomials.