Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C)

Let G = P Sp(2n, C) ( n 3 ) and 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 the flag variety G/B corresponding to w .Let Z(w, i) be the Bott-Samelson-Demazure-Hansen variety (the desingularization of X(w) ) corresponding to a reduced expression i of w .In this article, we study the cohomology groups of the tangent bundle on Z(w 0 , i) , where w 0 is the longest element of the Weyl group W .We describe all the reduced expressions i of w 0 in terms of a Coxeter element such that all the higher cohomology groups of the tangent bundle on Z(w 0 , i) vanish (see Theorem 8.1).