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arXiv · 2501.04432

A Relationship Between Character Values Of Wreath Products And The Symmetric Group

Rijubrata Kundu·Papi Ray
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Abstract

A relation between certain irreducible character values of the hyperoctahedral group $B_n$ ($\mathbb{Z}/2\mathbb{Z} \wr S_n$) and the symmetric group $S_{2n}$ was proved by F. L\"ubeck and D. Prasad in 2021. Their proof is algebraic in nature and uses Lie theory. Using combinatorial methods, R. Adin and Y. Roichman proved a similar relation between certain character values of $G\wr S_n$ and $S_{rn}$, where $G$ is an abelian group of order $r$ (generalizing the result of L\"ubeck-Prasad). Using their result, we prove yet another relation between certain irreducible character values of $G\wr S_n$ and $S_{rn}$, where $G$ is an abelian group of order $r$.

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Rijubrata Kundu, Papi Ray. 2025-01-08. A Relationship Between Character Values Of Wreath Products And The Symmetric Group. https://arxiv.org/abs/2501.04432

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