特征标的本原诱导次数

Primitive induced degrees of characters

在有限群表示论中,研究一个给定的不可约复特征标何时具有相同的本原诱导次数是一个基本而重要的问题.证明了一个三元组的特征标与其线性极限的极小诱导次数集合相同,从而加强了Dade关于初等稳定子极限的定理,给出了若干应用,并证明了三元组的任意两个线性极限都有相同的次数.

In the representation theory of finite groups,it is a basic and important problem to study that when a given character has the same primitive induced degree.It is proved that a character triple has the same primitive inducing degree as its any linear limit.This strengthenes the Dade's theorem and several applications are given.Also,it is proved that any two linear limits of the triple have the same degree.