The classification of Zamolodchikov periodic quivers
The classification of Zamolodchikov periodic quivers
复制标题
Zamolodchikov周期性颤动的分类
DOI：
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发表时间：
2016
影响因子：
1.7
通讯作者：
P. Pylyavskyy
中科院分区：
文献类型：
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作者：
Pavel Galashin;P. Pylyavskyy
翻译后摘要：Zamolodchikov周期性是一个属性的某些离散动力系统与颤抖。凯勒已经证明，对于作为两个丹金图的乘积而得到的箭图，它也成立。我们证明了具有Zamolodchikov周期性的箭图与有限型交换Cartan矩阵对是双射的。Stembridge在他的$W$-图的研究中对这种对进行了分类。该分类包括产品的Dynkin图沿着与其他四个无限的家庭，和八个例外情况。我们提供了一个证明Zamolodchikov周期性的所有四个剩余的无限家庭，并使用计算机程序验证的例外情况。
Abstract:Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity are in bijection with pairs of commuting Cartan matrices of finite type. Such pairs were classified by Stembridge in his study of $W$-graphs. The classification includes products of Dynkin diagrams along with four other infinite families, and eight exceptional cases. We provide a proof of Zamolodchikov periodicity for all four remaining infinite families, and verify the exceptional cases using a computer program.