McKay箭图与覆盖空间

本文研究在自然扩张和嵌入下特殊线性群和一般线性群的有限子群的McKay 箭图间的关系. 我们证明在特定条件下, 一般线性群GL(m;C) 的有限子群G的McKay 箭图是其正规子群G∩SL(m;C)的McKay 箭图的正则覆盖, 而当把G 嵌入SL(m+1;C) 时, 新的McKay 箭图由在原来的McKay 箭图的每一顶点加上一个由其Nakayama 平移到其自身的箭向得到. 作为例子, 我们指出如何用这些方法得到一些有趣的McKay 箭图.

On McKay quivers and covering spaces

In this paper,we study the relationship between the McKay quivers of finite subgroups of special linear groups and of general linear groups,via natural extension and embedding.We show that under certain condition,the McKay quiver of a finite subgroup G of GL（m,C） is a regular covering of the McKay quiver of its normal subgroup G ∩ SL（m,C）,and when embedding G in a canonical way into SL（m ＋ 1,C）,the new McKay quiver is obtained by adding an arrow from the Nakayama translation of i back to i for each vertex i.We also show by examples that certain interesting McKay quivers can be obtained in these ways.