Authors derive combinatorial descriptions for the number of inequivalent irreducible rational representations of GL_2(q) by degree and an explicit q-dependent formula for the Wedderburn decomposition of its rational group algebra.
Wedderburn decomposition of the rational group algebras of $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$
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abstract
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 $\operatorname{PSL}_2(q)$.
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On rational representations and rational group algebra of $\operatorname{GL}_2(q)$
Authors derive combinatorial descriptions for the number of inequivalent irreducible rational representations of GL_2(q) by degree and an explicit q-dependent formula for the Wedderburn decomposition of its rational group algebra.