Small Resolutions of Schubert Varieties in Symplectic and Orthogonal Grassmannians

Abstract

Let G be a semisimple algebraic group over C, and B a Borel subgroup of G. Let P be a parabolic subgroup of G that contains B. Denote by W the Weyl group of G with respect to a fixed maximal torus T c B, and let WP a W be the Weyl group of P. We denote the set of minimal representatives of W/Wp by W. For coeW, X(co) denotes the Schubert variety in G/P corresponding to co. X(co) is the Zariski closure of the B-orbit of a unique T-fixed point ew of G/P. We call ew 'the centre' of X(a)). Our conventions for labelling the simple roots in W are the same as in [1].