A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$-groups
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913565798039552 |
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| author | Choudhary, Ram Karan Prajapati, Sunil Kumar |
| author_facet | Choudhary, Ram Karan Prajapati, Sunil Kumar |
| contents | In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic $p$-group $G$, where $p$ is any prime. We also provide a formula for counting irreducible rational representations of $G$ with distinct degrees and derive a method to explicitly obtain all inequivalent irreducible rational matrix representations of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$-groups Choudhary, Ram Karan Prajapati, Sunil Kumar Representation Theory Rings and Algebras In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic $p$-group $G$, where $p$ is any prime. We also provide a formula for counting irreducible rational representations of $G$ with distinct degrees and derive a method to explicitly obtain all inequivalent irreducible rational matrix representations of $G$. |
| title | A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$-groups |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2410.20933 |