Quasi-Isolated Elements in Reductive Groups

Abstract

A semisimple element s of a connected reductive group G is called quasi-isolated (respectively isolated) if C _G ( s ) (respectively ( s )) is not contained in a Levi subgroup of a proper parabolic subgroup of G . We study properties of quasi-isolated semisimple elements and give a classification in terms of the affine Dynkin diagram of G . Tables are provided for adjoint simple groups.

Key Words:

• Affine Dynkin diagram
• Isolated element
• Reductive groups
• Semisimple element

1991 Mathematics Subject Classification:

• Primary 20G99
• Secondary 20E45

ACKNOWLEDGMENTS

We wish to thank F. Digne, J. Michel and M. Enguehard for their valuable comments on this work.

Notes

^#Communicated by J. Alev.