Displaying similar documents to “Noncrossing partitions, clusters and the Coxeter plane.”

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...

A Relation between the Weyl Group W(e8) and Eight-Line Arrangements on a Real Projective Plane

Fukui, Tetsuo, Sekiguchi, Jiro (2007)

Serdica Journal of Computing

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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006. The Weyl group W(E8) acts on the con guration space of systems of labelled eight lines on a real projective plane. With a system of eight lines with a certain condition, a diagram consisting of ten roots of the root system of type E8 is associated. We have already shown the existence of a W(E8)-equivariant map of the totality of such diagrams...