On representation zeta function of special linear groups over finite principal ideal local rings

2023/12/21 by Uri Ronen, Ronen, Uri
Mathematics · #20Cxx #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2312.13569

openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the group algebras ℂ[SL₃(\mathbbF₃[t]/(t³))] and ℂ[SL₃(ℤ/27)] are not isomorphic, as well as ℂ[SL₄(\mathbbF₂[t]/(t³))] and ℂ[SL₄(ℤ/8)], by computing the number of conjugacy classes in those groups using MAGMA's calculator. Similarly, we reproduce special cases of a recent result by Hassain and Singla, showing that ℂ[SL₂(\mathbbF₂[t]/(t^k))]\ncongℂ[SL₂(ℤ/2^k)] for 3≤ k≤ 8.

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