对称群S_(4)的表示环  

On the Green ring of symmetric groups S_(4)

作　　者：周木森 戴莉兰 ZHOUMu-sen;DAI Li-lan(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2023年第2期57-63,共7页Journal of Guangzhou University:Natural Science Edition

摘　　要：文章利用有限群特征标理论计算了对称群S_(4)的二维和三维不可约表示幂公式,刻画了S_(4)上表示环r(S_(4)),并找到S_(4)在有理数域Q上表示代数r_(Q)(S_(4))的5个一维表示和5个中心本原幂等元。In this paper,we calculate the power formulas of two-dimensional and three-dimensional irreducible representations of symmetric group S_(4) by using the character theory of finite group,characterize the Green ring r(S_(4))of S_(4),and find five one-dimensional representations and five central primitive idempotents of representation algebra r Q(S_(4))over the rational field Q.

关 键 词：对称群 群特征标 不可约表示 表示环 

分 类 号：O187.2[理学—数学]