Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups $SL_2(K)$
Trudy Instituta matematiki, Tome 31 (2023) no. 2, pp. 57-62.

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

Under certain restrictions, Weyl submodules with small highest weights in the restrictions of irreducible representations of simple algebraic groups to subsystem subgroups of type $A_1$ over a field of positive characteristic are found.
@article{TIMB_2023_31_2_a6,
     author = {A. A. Osinovskaya},
     title = {Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups $SL_2(K)$},
     journal = {Trudy Instituta matematiki},
     pages = {57--62},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_2_a6/}
}
TY  - JOUR
AU  - A. A. Osinovskaya
TI  - Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups $SL_2(K)$
JO  - Trudy Instituta matematiki
PY  - 2023
SP  - 57
EP  - 62
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2023_31_2_a6/
LA  - ru
ID  - TIMB_2023_31_2_a6
ER  - 
%0 Journal Article
%A A. A. Osinovskaya
%T Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups $SL_2(K)$
%J Trudy Instituta matematiki
%D 2023
%P 57-62
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2023_31_2_a6/
%G ru
%F TIMB_2023_31_2_a6
A. A. Osinovskaya. Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups $SL_2(K)$. Trudy Instituta matematiki, Tome 31 (2023) no. 2, pp. 57-62. http://geodesic.mathdoc.fr/item/TIMB_2023_31_2_a6/

[1] Shchigolev V., “A local criterion for Weyl modules for groups of type A”, Journal of Pure and Applied Algebra, 213:9 (2009), 1681–1701 | DOI | MR | Zbl

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

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

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

[5] Burbaki N., Gruppy i algebry Li, gl. IV–VI, Mir, M., 1972 | MR

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

[7] Smith S., “Irreducible modules and parabolic subgroups”, J. Algebra, 75 (1982), 286–289 | DOI | 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] 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