  We introduce the notion of a cominuscule point in a Schubert variety in a
generalized flag variety for a semisimple group. We derive formulas expressing
the Hilbert series and multiplicity of a Schubert variety at a cominuscule
point in terms of the restrictions of classes in torus-equivariant K-theory and
cohomology to that point, generalizing previously known formulas for flag
varieties of cominuscule type. Thus, we can calculate Hilbert series and
multiplicities in cases where these were previously unknown. The formulas for
Schubert varieties are special cases of more general formulas valid at
generalized cominuscule points of schemes with torus actions.
