| 对称群S5的表示环 |
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| 引用本文： | 戴莉兰,黎允楠.对称群S5的表示环[J].数学年刊A辑(中文版),2023,44(2):133-146. |
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| 作者姓名： | 戴莉兰 黎允楠 |
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| 作者单位： | 广州大学数学与信息科学学院, 广州 510006 |
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| 基金项目： | 国家自然科学基金(No.12071094, No.12171155) |
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| 摘 要： | 本文利用有限群特征标理论计算了对称群S5的所有不可约复表示的幂公式.根据求解幂公式过程中得到的S5任意两个不可约表示张量积的分解情况,作者刻画了S5上表示环r(S5)及其若干结构性质,如极小生成元关系式表达、单位群、本原幂等元、行列式与Casimir数.
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| 关 键 词： | 群特征标 对称群 Kronecker积 表示环 |
| 收稿时间： | 2022/8/31 0:00:00 |
| 修稿时间： | 2022/12/25 0:00:00 |
On the Representative Ring of the Symmetric Group S5 |
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| DAI Lilan,LI Yunnan.On the Representative Ring of the Symmetric Group S5[J].Chinese Annals of Mathematics,2023,44(2):133-146. |
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| Authors: | DAI Lilan LI Yunnan |
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| Institution: | School of Mathematics and Information Science, Guangzhou University,Guangzhou 510006, China. |
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| Abstract: | In this paper, the power formulas of all irreducible complex representations of symmetric group S5 are calculated by using the character theory of finite groups. According to the irreducible decomposition of tensor products of any two irreducible representations of S5 obtained in the process of solving the power formulas, the authors describe the complex representation ring r(S5) of S5 and several of its properties, such as an expression of minimal generators and defining relations, its unit group, primitive idempotents and its determinant and Casimir number. |
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| Keywords: | Group character Symmetric group Kronecker product Representation ring |
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