正规三元组上的模特征标性质

The Properties of Modular Characters on Normal Triples

在有限群模表示理论中,模特征标诱导和限制下的动态表现以及对应关系是有意义的问题,尤其是考虑如何把常表示的结论推广到模表示上,得到相应的模特征标结果一直是表示论中的重要课题.对于有限群G,如果N和M均为G的正规子群且N包含M,M.L.Lewis称(G,N,M)为群G的正规三元组,并且对其上的常特征标问题进行了探讨.首先给出了模特征标的一些基本性质,然后在正规三元组(G,N,M)条件下,得到了IBr(N)和IBr(M)中元素限制和诱导的若干动态表现,讨论了其上不可约模特征标的不变性和唯一性问题,并且进一步获得了互素正规三元组(X,N,M)上的几个模特征标对应关系.

In the modular representations of finite groups, it is profound to research the restriction,induction and correspondences of modular characters, especially for generalizing the relevant results of modular characters from the results of ordinary characters. Let G be a finite group,if N and M are both normal subgroups of G,and N M,then M. L. Lewis called （G,N,M） a normal triple of G and investigated the problems of ordinary characters about it. In this paper, some basic properties of modular characters are firsdy studied, then under the condition of the normal triple （G, N, M）, some results about the restriction and induction of the elements of IBr （N） and IBr（M） are given. Furthermore, some correspondences of modular characters about the coprime normal triple （X, N,M） are obtained.