特征标的Navarro顶点及应用简介  

A Brief Introduction to Navarro Vertices of Characters and Their Applications

作　　者：靳平 JIN Ping(School of Mathematics and Statistics,Shanxi University,Taiyuan,Shanci,030006,P.R.China)

机构地区：[1]山西大学数学与统计学院,山西太原030006

出　　处：《数学进展》2025年第2期343-356,共14页Advances in Mathematics(China)

基　　金：国家自然科学基金(Nos.12431001,12171289)。

摘　　要：2002年,Navarro使用Isaacs创立的特征标π-理论,特别是其中特征标的乘法分解技术,对p-可解群G的每个不可约复特征标χ∈Irr(G)定义了一个共轭唯一的特征标对(Q,δ),称为χ的Navarro顶点,其中Q为G的p-子群且δ∈Irr(Q).近年来许多学者探讨了Navarro顶点的诸多性质及应用,并用之研究有限群表示论中若干著名的局部—整体计数猜想.本文简介Navarro的顶点理论及其若干推广,阐述其在McKay猜想、Alperin权猜想、Cossey猜想以及Brauer特征标的提升问题中的应用,包含了我们最近所做的工作,并提出一些相关的研究问题.In 2002,Navarro used theπ-theory of characters founded by Isaacs,especially its multiplication decomposition technique,to define a unique up to conjugacy character pair(Q,δ)for each irreducible complex characterχ∈Irr(G)of a p-solvable group G,called the Navarro vertex of x,where Q is a p-subgroup of G andδ∈Irr(Q).In recent years many scholars have discussed properties of Navarro vertices with applications to several famous local-global counting conjectures in the representation theory of finite groups.In this paper we present a brief introduction to Navarro's vertex theory and its generalizations,stated some applications to the McKay conjecture,the Alperin weight conjecture,Cossey'conjecture and the lifting problem of Brauer characters.Our recent work is also included and some questions are raised.

关 键 词：Navarro顶点 广义顶点 BRAUER特征标 p-可分解的特征标 特征标的提升 

分 类 号：O152[理学—数学]