Geodesic
Models for the complex representations of the groups~$\operatorname{GL}(n,q)$
Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 365-379

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The main result of the paper consists in the construction of a model of the full linear group over a finite field, i.e. its representations such that each irreducible representation occurs as a component precisely once. The series of representations thus constructed has the well-known Gel'fand–Graev representation as first term. Bibliography: 12 titles. 
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     title = {Models for the complex representations of the groups~$\operatorname{GL}(n,q)$},
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A. A. Klyachko. Models for the complex representations of the groups~$\operatorname{GL}(n,q)$. Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 365-379. http://geodesic.mathdoc.fr/item/SM_1984_48_2_a5/