| 戴莉兰,黎允楠.对称群S5的表示环*[J].数学年刊A辑,2023,44(2):133~146 |
| 对称群S5的表示环* |
| On the Representative Ring of the Symmetric Group S5 |
| 投稿时间：2022-08-31 修订日期：2022-12-25 |
| DOI：10.16205/j.cnki.cama.2023.0011 |
| 中文关键词: 群特征标, 对称群, Kronecker积, 表示环 |
| 英文关键词:Group character, Symmetric group, Kronecker product, Representation ring |
| 基金项目:国家自然科学基金(No.12071094, No.12171155) |
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| 摘要点击次数: 690 |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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