About Knop's action of the Weyl group on the set of the set of orbits of a spherical subgroup in the flag manifold
Abstract
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 representation theory 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402390
 Bibcode:
 2004math......2390R
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Group Theory;
 20G20