Rank-metric separation in irreducible representations of finite groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908728444321792 |
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| author | Dvir, Zeev |
| author_facet | Dvir, Zeev |
| contents | We give a general lower bound on the rank of matrices of the form $ρ(h) - I$ with $ρ: G \rightarrow GL({\mathbb F}^n)$ an irreducible representation of a finite group $G$. The main tool in the proof is a (strengthening) of a reduction due to Efremenko from low rank matrices spanned by a few images of $ρ$ to Locally Decodable Codes (LDCs), which are a special kind of error correcting codes. We then apply the known results on 2-query LDCs to derive our rank bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rank-metric separation in irreducible representations of finite groups Dvir, Zeev Group Theory Combinatorics Representation Theory We give a general lower bound on the rank of matrices of the form $ρ(h) - I$ with $ρ: G \rightarrow GL({\mathbb F}^n)$ an irreducible representation of a finite group $G$. The main tool in the proof is a (strengthening) of a reduction due to Efremenko from low rank matrices spanned by a few images of $ρ$ to Locally Decodable Codes (LDCs), which are a special kind of error correcting codes. We then apply the known results on 2-query LDCs to derive our rank bound. |
| title | Rank-metric separation in irreducible representations of finite groups |
| topic | Group Theory Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2512.19638 |