Parabolic subgroups and automorphism groups of Schubert varieties

Abstract

Let G be a simple algebraic group of adjoint type over the field C of complex numbers, B be a Borel subgroup of G containing a maximal torus T of G. Let w be an element of the Weyl group W and X(w) be the Schubert variety in G/B corresponding to w. In this article we show that given any parabolic subgroup P of G containing B properly, there is an element w∈W such that P is the connected component, containing the identity element of the group of all algebraic automorphisms of X(w).