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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Rudakov A. N., Shafarevich I. R., “Neprivodimye predstavleniya trekhmernoi prostoi algebry Li nad polem polozhitelnoi kharakteristiki”, Matem. zametki, 2:5 (1967), 439–454 | MR | Zbl

[2] Diksme Zh., Universalnye obertyvayuschie algebry, Mir, M., 1978 | MR

[3] Zassenhaus H., “The representations of Lie algebras in prime characteristic”, Proc. Glasgow Math. Assoc, 2 (1954), 1–36 | DOI | MR | Zbl

[4] Rudakov A. N., “O predstavleniyakh klassicheskikh poluprostykh algebr Li v pole polozhitelnoi kharakteristiki”, Izv. AN SSSR. Ser. matem., 34:4 (1970), 735–743 | MR | Zbl

[5] Veldkamp F. D., “The center of the universal enveloping, algebra of a Liealgebra incharacteristic $p$”, Ann. sci. Ecole norm. super., 5:2 (1972), 217–240 | MR | Zbl

[6] Springer T., Teoriya invariantov, Mir, M., 1981 | MR | Zbl

[7] Seminar po algebraicheskim gruppam, Mir, M., 1973 | MR