RESTRICTIONS OF REPRESENTATIONS OF ALGEBRAIC GROUPS OF TYPES E_n AND F₄ TO NATURALLY EMBEDDED A₁-SUBGROUPS AND THE BEHAVIOR OF ROOT ELEMENTS

ABSTRACT

Modular irreducible p -restricted representations of algebraic groups of types E _n (n=6, 7, 8) and F ₄ are studied. The composition factors of the restrictions of such representations to naturally embedded A ₁-subgroups are found. Jordan block sizes of root unipotent elements of such groups in the representations with locally small highest weights with respect to p are determined.

Key Words:

• Algebraic groups
• Jordan blocks
• Representations
• Restrictions to subgroups
• Unipotent elements

Mathematics Subject Classification:

• 20G05

ACKNOWLEDGMENTS

The author is grateful to I. D. Suprunenko for a permanent attention to this work and useful comments.

The research was supported by the Institute of Mathematics of the National Academy of Sciences of Belarus in the framework of the State Basic Research Programme “Mathematical Structures.”

Notes

^#Communicated by B. Parshall.