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.
No takes yet. Share an insight, caveat, or question.
Cédric Bonnafé (2005) studied this question.