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.
Publié le : 2004-02-24
Classification:
Knop's action,
Borel subgroup,
spherical subgroup,
20G20,
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
@article{hal-00001181,
author = {Ressayre, Nicolas},
title = {About Knop's action of the Weyl group on the setof the set of orbits of a spherical subgroup in the flag manifold},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00001181}
}
Ressayre, Nicolas. About Knop's action of the Weyl group on the setof the set of orbits of a spherical subgroup in the flag manifold. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00001181/