Parabolic subgroups with Abelian unipotent radical.

R. Richardson; G. Röhrle; R. Steinberg

Displaying similar documents to “Parabolic subgroups with Abelian unipotent radical.”

The Invariants of Unipotent Radicals of Parabolic Subgroups.

F.D. Grosshans (1983)

Inventiones mathematicae

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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...