Displaying similar documents to “A note on parabolic subgroups.”

On normal abelian subgroups in parabolic groups

Gerhard Röhrle (1998)

Annales de l'institut Fourier

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Let G be a reductive algebraic group, P a parabolic subgroup of G with unipotent radical P u , and A a closed connected subgroup of P u which is normalized by P . We show that P acts on A with finitely many orbits provided A is abelian. This generalizes a well-known finiteness result, namely the case when A is central in P u . We also obtain an analogous result for the adjoint action of P on invariant linear subspaces of the Lie algebra of P u which are abelian Lie algebras. Finally, we discuss...