Geodesic
Composition factors of the restrictions of modular representations of $SL_{r+1}(K)$ to semisimple subgroups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 113-124 
A. A. Osinovskaya. Composition factors of the restrictions of modular representations of $SL_{r+1}(K)$ to semisimple subgroups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 113-124. http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a6/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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. Under some minor restrictions on a group rank, the composition factors for such restrictions are described.

[1] T. M. Zheleznaya, “Ob ogranicheniyakh neprivodimykh predstavlenii algebraicheskikh grupp tipa $A_n$ v kharakteristike $0$ na podgruppy tipa $A_1 \times A_1$”, Trudy Instituta matematiki, 15:1 (2007), 56–67 | Zbl

[2] A. E. Zalesskii, I. D. Suprunenko, “Usechennye simmetricheskie stepeni estestvennykh realizatsii grupp $SL_m (P)$ i $Sp_m (P)$ i ikh ogranicheniya na podgruppy”, Sibirskii matematicheskii zhurnal, 31:4 (1990), 33–46 | MR | Zbl

[3] A. A. Osinovskaya, “Ogranicheniya modulyarnykh predstavlenii spetsialnykh lineinykh grupp na podgruppy tipa $A_1\times A_1$”, Sibirskii matematicheskii zhurnal, 51:5 (2010), 1120–1128 | MR | Zbl

[4] A. A. Premet, “Vesa infinitezimalno neprivodimykh predstavlenii nad polem prostoi kharakteristiki”, Matem. sbornik, 133:2 (1987), 167–183

[5] R. Steinberg, Lektsii o gruppakh Shevalle, Mir, M., 1975

[6] I. D. Suprunenko, “Sokhranenie sistem vesov neprivodimykh predstavlenii algebraicheskoi gruppy i algebry Li tipa $A_l$ s ogranichennymi vesami pri reduktsii po modulyu $p$”, Izv. AN BSSR, seriya fiz.-mat. nauk, 1983, no. 2, 18–22 | Zbl

[7] J. Brundan, A. S. Kleshchev, I. D. Suprunenko, “Semisimple restrictions from $GL(n)$ to $GL(n-1)$”, J. für die reine und angew. Math., 500 (1998), 83–112 | MR | Zbl

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

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

[10] A. A. Osinovskaya, “The restrictions of representations of special linear groups to subsystem subgroups of type $A_1\times A_1$”, Trudy Instituta matematiki, 29:1–2 (2021), 175–187 | MR

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

[12] I. D. Suprunenko, 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