On Normal Abelian Subgroups in Parabolic Groups
نویسنده
چکیده
Let G be a reductive algebraic group, P a parabolic subgroup of G with unipotent radical Pu, and A a closed connected unipotent subgroup of Pu which is normalized by P. We show that P acts on A with nitely many orbits provided A is abelian. This generalizes a well-known niteness result, namely the case when A is central in Pu. We also obtain an analogous result for the adjoint action of P on invariant linear subspaces which are abelian as subalgebras of the Lie algebra of Pu. Finally, we discuss a connection to some work of Mal'cev on abelian subalgebras of the Lie algebra of G.
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