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arXiv · 2408.04921

Irreducible characters of the generalized symmetric group

Huimin Gao·Naihuan Jing
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Abstract

The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the Ariki-Koike version of the Murnaghan-Nakayama rule by vertex algebraic methods, 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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BibTeXRIS

Huimin Gao, Naihuan Jing. 2024-08-09. Irreducible characters of the generalized symmetric group. https://arxiv.org/abs/2408.04921

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