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We consider a desingularization Gamma of a Richardson variety X_w^v=X_w \capX^v in the flag variety Fl(n)=GL(n)/B, obtained as a fibre of a projection froma certain Bott-Samelson variety Z. We then construct a basis of the homogeneouscoordinate ring of Gamma inside Z, indexed by combinatorial objects which wecall w_0-standard tableaux.

Standard Monomial Theory for desingularized Richardson varieties in the flag variety GL(n)/B