Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors I
Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors I
复制标题
子因子 I 网络的模不变量、图和 α 归纳¶
DOI：
10.1007/s002200050455
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发表时间：
1998
影响因子：
2.4
通讯作者：
David E. Evans
中科院分区：
文献类型：
--
作者：
Jens Böckenhauer;David E. Evans
摘要：我们分析了Longo和Rehren定义的子要素网的扇区的诱导和制约。通过选取一个局部子因子，我们得到了一个公式，它用较小的网和正则自同态的原始DHR扇区来描述诱导扇区的结构。我们还得到了诱导和扇区限制的倒易公式，并证明了诱导映射的某种同态性质。在即将发表的一篇文章中，我们将把这一理论应用于由共形场理论产生的子因子网，特别是来自SU(N)WZW模型的共形嵌入或或分支包含的子因子网。这将有助于更好地理解某些图对模不变量的标号，特别是对SU(2)模不变量的A-D-E分类。
Abstract: We analyze the induction and restriction of sectors for nets of subfactors defined by Longo and Rehren. Picking a local subfactor we derive a formula which specifies the structure of the induced sectors in terms of the original DHR sectors of the smaller net and canonical endomorphisms. We also obtain a reciprocity formula for induction and restriction of sectors, and we prove a certain homomorphism property of the induction mapping.Developing further some ideas of F. Xu we will apply this theory in a forthcoming paper to nets of subfactors arising from conformal field theory, in particular those coming from conformal embeddings or orbifold inclusions of SU(n) WZW models. This will provide a better understanding of the labelling of modular invariants by certain graphs, in particular of the A-D-E classification of SU(2) modular invariants.