特征标的诱导源与复合Clifford对应  

Inductive Sources and Compound Clifford Correspondence of Characters

作　　者：靳平[1] 温馨 JIN Ping;WEN Xin(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院

出　　处：《山西大学学报（自然科学版）》2019年第4期804-810,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11601289);山西省自然科学基金(201601D011006)

摘　　要：作为正规子群和Clifford对应的推广,Dade引入了诱导源和诱导源对应的概念,给出了诱导源的一个判别条件,并证明了特征标三元组的诱导源对应在奇数条件下等同于复合Clifford对应。随后Isaacs和Lewis以及Loukaki对诱导源做了更多的研究。文章研究诱导源的判别问题,得到了一个特征标对是诱导源的若干充要条件,加强了Dade的相关结果,还推广了Dade关于诱导源与复合Clifford对应的定理。特别地,文章所使用的方法不仅简化了Dade的原始证明,去掉了对双曲模的依赖,而且还是纯特征标理论的。As generalizations of normal subgroups and the Clifford correspondence, Dade introduced the concepts of inductive sources and the inductive source correspondence, presented a discriminant condition of inductive sources, and proved that inductive sources of a character triple coincides with the compound Clifford correspondence under some oddness conditions.Subsequently,Isaacs, Lewis and Loukaki made more research. In this paper,the discrimination problem for inductive sources was studied, some necessary and sufficient conditions for a character pair to be an inductive source wert obtained, which strengthened the related result of Dade. Moreover, the above theorem of Dade about inductive sources and the compound Clifford correspondence was generalized. In particular, the method used in the paper not only simplifies Dade’s original proof and removes the dependence on hyperbolic modules, but also is purely character theoretic.

关 键 词：诱导源 诱导源对应 复合Clifford对应 特征标三元组 

分 类 号：O152.6[理学—数学]