We construct an explicit basis for the coordinate ring of the Bott-Samelson
variety Z_i associated to G = GL(n) and an arbitrary sequence of simple
reflections i. Our basis is parametrized by certain standard tableaux and
generalizes the Standard Monomial basis for Schubert varieties. Our standard
tableaux have a natural crystal graph structure.Comment: Northeastern University, [email protected] AMSTeX amspp