广义对称群的不可减字符

arXiv - MATH - Representation Theory Pub Date : 2024-08-09 DOI:arxiv-2408.04921

Huimin Gao, Naihuan Jing

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引用次数: 0

摘要

本文研究了如何通过迭代算法计算广义对称群 $C_k\wr{S}_n$ 的不可约字符。在用顶点代数方法重现了穆纳汉-中山规则之后，我们提出了广义对称群字符的新迭代公式。在应用中，我们发现了$C_k\wr S_n$ 的字符值与$S_{kn}$ 的模块字符之间的数值关系。

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Irreducible characters of the generalized symmetric group

The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the Murnaghan-Nakayama rule by vertex algebraic method, we formulate a new iterative formula for characters of the generalized symmetric group. As applications, we find a numerical relation between the character values of $C_k\wr S_n$ and modular characters of $S_{kn}$.

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arXiv - MATH - Representation Theory

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