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On normal abelian subgroups in parabolic groups

Gerhard Röhrle — 1998

Annales de l'institut Fourier

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 a connection...

Infinitesimal unipotent group schemes of complexity 1

Rolf Farnsteiner; Gerhard Röhrle; Detlef Voigt — 2001

Colloquium Mathematicae

We classify the uniserial infinitesimal unipotent commutative groups of finite representation type over algebraically closed fields. As an application we provide detailed information on the structure of those infinitesimal groups whose distribution algebras have a representation-finite principal block.

MOP -- algorithmic modality analysis for parabolic actions.

Jürgens, Ulf; Röhrle, Gerhard — 2002

Experimental Mathematics

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On normal abelian subgroups in parabolic groups

Infinitesimal unipotent group schemes of complexity 1

MOP -- algorithmic modality analysis for parabolic actions.