一类特殊三部分标准抛物子群幂幺根基的特征标

奕可 李(武汉轻工大学，中国)
朔 刘(武汉轻工大学，中国)
晓磊 方(武汉轻工大学，中国)

摘要

本文完整刻画了GL6对应划分为(2,2,2)的标准抛物子群的一类特殊幂幺根基GE的所有不可约表示. 通过运用阿贝尔正规子群半直积的Clifford理论, 从共伴随轨道成功构建了该群的全部不可约特征标, 并将其按维数进行精确分类. 研究结果表明: 对于任意固定维数,GE的不可约表示的个数均可表示为q−1的非负整系数多项式函数. 这一重要发现不仅揭示了该类群表示的数量规律, 更从严格数学意义上验证了Higman、Lehrer和Isaacs提出的关于有限群表示猜想的模拟猜想, 为相关理论的发展提供了新的例证和支持。

关键词

共伴随轨道；pattern群；上三角群；Higman猜想

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DOI: http://dx.doi.org/10.12345/bdai.v6i6.34041