The restrictions of representations of special linear groups to subsystem subgroups of type $A_1\times A_1$
Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 176-188.

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The restrictions of irreducible representations of the special linear group over an algebraically closed field of positive characteristic $p$ to subsystem subgroups of type $A_1\times A_1$ are studied. The symmetry of the set of highest weights of composition factors is proven. The "big" composition factors of such restrictions for the arbitrary $p$-restricted representations are found. These results will be used for the complete description of such restrictions.
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A. A. Osinovskaya. The restrictions of representations of special linear groups to subsystem subgroups of type $A_1\times A_1$. Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 176-188. http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a15/

[1] Bourbaki N., Groupes et algèbres de Lie, Chaps. VII–VIII, Hermann, Paris, 1975 | MR

[2] Jantzen J.C., Representations of Algebraic Groups, Second edition, Amer. Math. Soc., Providence, 2003 | MR | Zbl

[3] Osinovskaya A.A., “Restrictions of irreducible representations of classical algebraic groups to root $A_1$-subgroups”, Commun. in Algebra, 31:5 (2003), 2357–2379 | DOI | MR | Zbl

[4] Osinovskaya A.A., “Restrictions of modular representations of special linear groups to $A_1\times A_1$-subgroups”, Siberian Mathematical Journal, 51:5 (2010), 892–898 | DOI | MR | Zbl

[5] Osinovskaya A.A., “The restrictions of representations of the special linear group to subsystem subgroups of type $A_2$”, Journal of Mathematical Sciences, 234:3 (2018), 203–218 | DOI | MR | Zbl

[6] Shchigolev V., “Weyl submodules in restrictions of simple modules”, J. Algebra, 321 (2009), 1453–1462 | DOI | MR | Zbl

[7] Steinberg R., Lectures on Chevalley groups, Mimeographed Lecture Notes, Yale Univ. Press, 1968 | MR | Zbl

[8] Suprunenko I.D., The minimal polynomials of unipotent elements in irreducible representations of the classical groups in odd characteristic, Memoirs of the AMS, 200, no. 939, 2009 | DOI | MR

[9] Zheleznaya T.M., “On the restrictions of irreducible representations of algebraic groups of type $A_n$ in characteristic $0$ to subgroups of type $A_1 \times A_1$”, Trudy Instituta matematiki, 15:1 (2007), 56–67 (in Russian) | Zbl