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Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups SL2(K)

Abstract

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.

About the Author

A. A. Osinovskaya
Институт математики НАН Беларуси
Belarus


References

1. Shchigolev V. A local criterion for Weyl modules for groups of type A // Journal of Pure and Applied Algebra. 2009. Vol. 213, N 9. P. 1681–1701.

2. Shchigolev V. Weyl submodules in restrictions of simple modules // J. Algebra. 2009. Vol. 321. P. 1453–1462.

3. Osinovskaya A. A. The restrictions of representations of special linear groups to subsystem subgroups of type A1 ×A1 // Тр. Ин-та математики. 2021. Т. 29, № 1–2. С. 175–187.

4. Стейнберг Р. Лекции о группах Шевалле. М.: Мир, 1975.

5. Бурбаки Н. Группы и алгебры Ли, гл. IV–VI. М.: Мир, 1972.

6. Jantzen J. C. Representations of Algebraic Groups. Second edition. Providence: Amer. Math. Soc., 2003.

7. Smith S. Irreducible modules and parabolic subgroups // J. Algebra. 1982. Vol. 75. P. 286–289.

8. Suprunenko I. D. The minimal polynomials of unipotent elements in irreducible representations of the classical groups in odd characteristic // Memoirs of the AMS. 2009. Vol. 200, N 939.

9. Osinovskaya A. A. Restrictions of irreducible representations of classical algebraic groups to root A1-subgroups // Commun. in Algebra. 2003. Vol. 31, N 5. P. 2357–2379.


Review

For citations:


Osinovskaya A.A. Weyl submodules in the restrictions of representations of simple algebraic groups to subgroups SL2(K). Trudy Instituta matematiki. 2023;31(2):57-62. (In Russ.)

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ISSN 1812-5093 (Print)