Counting Irreducible Representations of a Finite Abelian Group
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909582515765248 |
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| author | Breuer, Thomas Kumar, Prashun Venkataraman, Geetha |
| author_facet | Breuer, Thomas Kumar, Prashun Venkataraman, Geetha |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting Irreducible Representations of a Finite Abelian Group Breuer, Thomas Kumar, Prashun Venkataraman, Geetha Group Theory 20H30, 20K01, 20K27, 20K30 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. |
| title | Counting Irreducible Representations of a Finite Abelian Group |
| topic | Group Theory 20H30, 20K01, 20K27, 20K30 |
| url | https://arxiv.org/abs/2504.12787 |