Displaying similar documents to “Tight quotients and double quotients in the Bruhat order.”

The closure diagram for nilpotent orbits of the split real form of E8

Dragomir Đoković (2003)

Open Mathematics

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Let 𝒪 1 and 𝒪 2 be adjoint nilpotent orbits in a real semisimple Lie algebra. Write 𝒪 1 ≥ 𝒪 2 if 𝒪 2 is contained in the closure of 𝒪 1 . This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split real form of the simple complex Lie algebra, E 8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present a comprehensive list of simple representatives of these orbits, and...

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...