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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2501.04432 |
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| _version_ | 1866929665256456192 |
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| author | Kundu, Rijubrata Ray, Papi |
| author_facet | Kundu, Rijubrata Ray, Papi |
| contents | 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. Lübeck 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 Lübeck-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 $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Relationship Between Character Values Of Wreath Products And The Symmetric Group Kundu, Rijubrata Ray, Papi Combinatorics Representation Theory 20C30, 20E22, 05E10 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. Lübeck 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 Lübeck-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 $r$. |
| title | A Relationship Between Character Values Of Wreath Products And The Symmetric Group |
| topic | Combinatorics Representation Theory 20C30, 20E22, 05E10 |
| url | https://arxiv.org/abs/2501.04432 |