Counting Irreducible Representations of a Finite Abelian Group

2025/04/17 by Thomas Breuer, Breuer, Thomas, Prashun Kumar +3
Computer Science · Mathematics · #20H30 #20K01 #20K27 #20K30 #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2504.12787

openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a power of a prime p, G be a finite abelian group, where p does not divide |G|,and let n be a positive integer. In this paper we find a formula for the number of irreducible representations of G of a given dimension n over the field of order q, up to equivalence, using Brauer characters. We also provide a formula for such n using the prime decomposition of the exponent of G and an algorithm to compute the irreducible degrees and their multiplicities.

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