This analysis finds a formula for irreducible representations in finite fields, indicating a method for evaluating degrees and multiplicities.
Let G be a finite abelian group and let n be a positive integer. In this paper we find a formula for the number of irreducible representations of G of dimension n over a given finite field, up to equivalence. 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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Breuer et al. (2025) studied this question.
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