论文标题
McKay图形用于交替组和古典组
McKay graphs for alternating and classical groups
论文作者
论文摘要
令$ g $为有限的群体，而$α$是$ g $的非平凡特征。 McKay Graph $ \ MATHCAL {M}（g，α）$具有$ G $的不可约字符，如果$χ_2$是$αχ_1$的组成部分。我们研究有限简单组$ g $的麦凯图的直径。对于交替组，我们证明了[lst]中的一个猜想：有一个绝对常数的$ c $，以至于$ \ hbox {diam} \，{\ Mathcal m}（g，g，α）\ le c \ le c \ frac {\ log | \ log | \ mathsf {a} _n} _n} _n |} $ y $ for -forred fon $ \ mathsf {a} _n $的of。同样，对于符合或正交类型的等级$ r $的班级组，我们在所有非平凡McKay图的直径上建立了线性上限$ CR $。
Let $G$ be a finite group, and $α$ a nontrivial character of $G$. The McKay graph $\mathcal{M}(G,α)$ has the irreducible characters of $G$ as vertices, with an edge from $χ_1$ to $χ_2$ if $χ_2$ is a constituent of $αχ_1$. We study the diameters of McKay graphs for finite simple groups $G$. For alternating groups, we prove a conjecture made in [LST]: there is an absolute constant $C$ such that $\hbox{diam}\,{\mathcal M}(G,α) \le C\frac{\log |\mathsf{A}_n|}{\log α(1)}$ for all nontrivial irreducible characters $α$ of $\mathsf{A}_n$. Also for classsical groups of symplectic or orthogonal type of rank $r$, we establish a linear upper bound $Cr$ on the diameters of all nontrivial McKay graphs.
