Standard Monomial Theory for desingularized Richardson varieties in the   flag variety GL(n)/B
  We consider a desingularization Gamma of a Richardson variety X_w^v=X_w \cap X^v in the flag variety Fl(n)=GL(n)/B, obtained as a fibre of a projection from a certain Bott-Samelson variety Z. We then construct a basis of the homogeneous coordinate ring of Gamma inside Z, indexed by combinatorial objects which we call w_0-standard tableaux. 
Micha\"el Balan
math.AG math.CO math.RT