不可约复特征标的顶点  

Vertices of Irreducible Complex Characters

作　　者：靳平[1] 赵建楠 JIN Ping;ZHAO Jiannan(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2021年第2期199-204,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11671238)。

摘　　要：设G为有限群,χ∈Irr (G)为不可约复特征标,作为不可约Brauer特征标的顶点的模拟,如何定义χ的顶点是目前群表示论中的一个重要问题。Cossey为了统一若干不同的顶点定义,在2008年给出了一般化的顶点构造,并在奇数阶群中证明了该顶点在共轭下是唯一的。文章减弱了群的奇数条件,在更为一般的π-可分群中证明了Cossey顶点在线性共轭下也是唯一的,并且在π-限制下也包含了经典的顶点子群,从而推广了Cossey的主要结果,拓宽了顶点理论的应用范围。Let G be a finite group, and χ ∈ Irr(G) be an irreducible complex character.As an analogue of the vertex of irreducible Brauer characters, how to define the vertex of χ is an important problem in the current group representation theory.In order to unify several different vertex definitions, Cossey gave a generalized vertex construction in 2008 and proved that the vertex is unique under conjugation in odd-order groups.In this paper, the oddness condition on groups is weakened and the Cossey vertex is also unique under linear conjugation in the more general π-separable groups.Moreover, it also includes the classical vertex subgroups when restricting to π-elements, thus generalizing the main result of Cossey and broadening the application scope of vertex theory.

关 键 词：Π-可分群 π-特殊的特征标 π-可分解的特征标 顶点 线性共轭 

分 类 号：O125.6[理学—数学]