  We give a closed-form formula for the Hilbert function of the tangent cone at
the identity of a Schubert variety X in the Grassmannian in both group
theoretic and combinatorial terms. We also give a formula for the multiplicity
of X at the identity, and a Grobner basis for the ideal defining the
intersection of X with the opposite cell as a closed subvariety of the opposite
cell. We give conjectures for the Hilbert function and multiplicity at points
other than the identity.
