Rank-metric separation in irreducible representations of finite groups

Zeev Dvir

doi:10.1016/j.laa.2026.06.010

Rank-metric separation in irreducible representations of finite groups

Zeev Dvir

Research output: Contribution to journal › Article › peer-review

Abstract

We give a general lower bound on the rank of matrices of the form ρ(h)−I with ρ:G→GL(Fⁿ) 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.

Original language	English (US)
Pages (from-to)	1-14
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	748
DOIs	https://doi.org/10.1016/j.laa.2026.06.010
State	Published - Nov 1 2026

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

Error correcting codes
Finite groups
Representations

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10.1016/j.laa.2026.06.010

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AB - We give a general lower bound on the rank of matrices of the form ρ(h)−I with ρ:G→GL(Fn) 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.

KW - Error correcting codes

KW - Finite groups

KW - Representations

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UR - https://www.scopus.com/pages/publications/105042283047#tab=citedBy

U2 - 10.1016/j.laa.2026.06.010

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SP - 1

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Rank-metric separation in irreducible representations of finite groups

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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