Geodesic
The restrictions of representations of the special linear group to subsystem subgroups of type $A_2$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 130-153 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The restrictions of irreducible representations of the special linear group over an algebraically closed field of positive characteristic $p$ to subsystem subgroups of type $A_2$ are studied. The composition factors for such restrictions are described in the case where the highest weights of the representations are locally small. 
@article{ZNSL_2017_455_a11,
     author = {A. A. Osinovskaya},
     title = {The restrictions of representations of the special linear group to subsystem subgroups of type~$A_2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {130--153},
     year = {2017},
     volume = {455},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a11/}
}
TY  - JOUR
AU  - A. A. Osinovskaya
TI  - The restrictions of representations of the special linear group to subsystem subgroups of type $A_2$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 130
EP  - 153
VL  - 455
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a11/
LA  - ru
ID  - ZNSL_2017_455_a11
ER  - 
%0 Journal Article
%A A. A. Osinovskaya
%T The restrictions of representations of the special linear group to subsystem subgroups of type $A_2$
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 130-153
%V 455
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a11/
%G ru
%F ZNSL_2017_455_a11
A. A. Osinovskaya. The restrictions of representations of the special linear group to subsystem subgroups of type $A_2$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 130-153. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a11/

[1] H. H. Andersen, J. C. Jantzen, W. Soergel, “Representations of quantum groups at a $p$th root of unity and of semisimple groups in characteristic $p$: independence of $p$”, Astérisque, 220 (1994), 1–321 | MR

[2] N. Burbaki, Gruppy i algebry Li, Gl. VII–VIII, Mir, M., 1978 | MR

[3] J. Brundan, A. Kleshchev, I. Suprunenko, “Semisimple restrictions from $\mathrm{GL}(n)$ to $\mathrm{GL}(n-1)$”, J. reine angew. Math., 500 (1998), 83–112 | MR | Zbl

[4] P. Fiebig, “An upper bound on the exceptional characteristics for Lusztig's character formula”, J. reine angew. Math., 673 (2012), 1–31 ; Preprint, 2008, arXiv: 0811.1674 | DOI | MR | Zbl

[5] R. Goodman, N. R. Wallach, Symmetry, representations, and invariants, Graduate texts in mathematics, 255, Springer, Dordrecht, 2009 | DOI | MR | Zbl

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

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

[8] A. A. Osinovskaya, “On the restrictions of modular irreducible representations of algebraic groups of type $A_n$ to naturally embedded subgroups of type $A_2$”, J. Group Theory, 8 (2005), 43–92 | DOI | MR | Zbl

[9] A. A. Osinovskaya, “Ogranicheniya modulei nad klassicheskimi gruppami na podgruppy tipa $A_2$ v kharakteristike 2”, Zap. nauchn. semin. POMI, 386, 2011, 227–241

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

[11] R. Steinberg, Lectures on Chevalley Groups, New Haven, 1968 | MR

[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, 154 pp. | DOI | MR

[13] A. E. Zalesskii, I. D. Suprunenko, “Usechennye simmetricheskie stepeni estestvennykh realizatsii grupp $\mathrm{SL}_m(P)$ i $\mathrm{Sp}_m(P)$ i ikh ogranicheniya na podgruppy”, Sibir. matem. zh., 31:4 (1990), 33–46 | MR