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Pré-Publication, Document De Travail Année : 2004

About Knop's action of the Weyl group on the setof the set of orbits of a spherical subgroup in the flag manifold

Résumé

Let $G$ be a complex connected reductive algebraic group.Let $G/B$ denote the flag variety of $G$. Let $H$ be an algebraic subgroup of $G$ such that the set ${\bf H}(G/B)$ of the $H$-orbits in $G/B$ is finite ; $H$ is said to be {\it spherical}.These orbits are of importance in representationtheory and in the geometry of the $G$-equivariant embeddings of $G/H$.In 1995, F. Knop has defined an action of the Weyl group $W$ of $G$ on ${\bf H}(G/B)$. The aim of this note is to construct natural invariants separating the $W$-orbits of Knop's action.
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Dates et versions

hal-00001181 , version 1 (24-02-2004)

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Nicolas Ressayre. About Knop's action of the Weyl group on the setof the set of orbits of a spherical subgroup in the flag manifold. 2004. ⟨hal-00001181⟩
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