Wedderburn decomposition of the rational group algebras of $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$
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| Format: | Preprint |
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2026
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| _version_ | 1866913041059151872 |
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| author | Choudhary, Ram Karan Panja, Saikat |
| author_facet | Choudhary, Ram Karan Panja, Saikat |
| contents | In this article, we derive explicit combinatorial formulas, depending only on $q$, for the Wedderburn decomposition of the rational group algebras of the finite linear groups $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$. Furthermore, we also determine the number of pairwise non-isomorphic simple $\mathbb Q G$-modules of each possible dimension for $G$ being either $\operatorname{SL}_2(q)$ or $\operatorname{PSL}_2(q)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16078 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wedderburn decomposition of the rational group algebras of $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$ Choudhary, Ram Karan Panja, Saikat Representation Theory Combinatorics Group Theory Rings and Algebras 20C05, 20G15, 20G05 In this article, we derive explicit combinatorial formulas, depending only on $q$, for the Wedderburn decomposition of the rational group algebras of the finite linear groups $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$. Furthermore, we also determine the number of pairwise non-isomorphic simple $\mathbb Q G$-modules of each possible dimension for $G$ being either $\operatorname{SL}_2(q)$ or $\operatorname{PSL}_2(q)$. |
| title | Wedderburn decomposition of the rational group algebras of $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$ |
| topic | Representation Theory Combinatorics Group Theory Rings and Algebras 20C05, 20G15, 20G05 |
| url | https://arxiv.org/abs/2604.16078 |