Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a field of positive characteristic

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.
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