Geodesic
Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a~field of positive characteristic
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 19-32

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The irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over an algebraically closed field of characteristic $p>n$ are described. It is proved that an irreducible representation has maximal dimension only if its central character is a nonsingular point of the Zassenhaus manifold. Bibliography: 7 titles. 
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A. N. Panov. Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a~field of positive characteristic. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 19-32. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a1/