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arXiv · 2410.20933

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$-groups

Ram Karan Choudhary·Sunil Kumar Prajapati
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Abstract

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 $G$.

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Ram Karan Choudhary, Sunil Kumar Prajapati. 2024-10-28. A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$-groups. https://arxiv.org/abs/2410.20933

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