Toric degenerations of Schubert varieties

LetG be a simply connected semisimple complex algebraic group. We prove that every Schubert variety ofG has a flat degeneration into a toric variety. This provides a generalization of results of [9], [7], [6]. Our basic tool is Lusztig's canonical basis and the string parametrization of this basis.Supported in part by the EC TMR network Algebraic Lie Representations, contract No. ERB FMTX-CT97-0100.