Let G be an almost simple, simply connected algebraic group over the field C of complex numbers. Let B be a Borel subgroup of G containing a maximal torus T of G, and let W be the Weyl group defined by T. The Borel group B determines a subset of simple reflections in W. For w in W, we let Z(w,i̲) be the Bott–Samelson–Demazure–Hansen variety corresponding to a reduced expression i̲ of w as a product of these simple reflections. In this article, we study the geometric invariant theoretic quotient of Z(w,i̲) for the T-linearized ample line bundles.
