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

摘要

Let G be a connected reductive algebraic group defined on an algebraically closed field k of characteristic different from 2. Let S denote the flag variety of G. Let H be a spherical subgroup of G. F. Knop defined an action of the Weyl group W of G on the finite set of the H-orbits in S. Here, we define an invariant, namely the type, separating the orbits of W.