  The set of T-invariant curves in a Schubert variety through a T-fixed point
is relatively easy to characterize in terms of its weights, but the tangent
space is more difficult. We prove that the weights of the tangent space are
contained in the rational cone generated by the weights of the T-invariant
curves. In simply laced types, this remains true if "rational" is replaced by
"integral". We also obtain conditions under which every weight of the tangent
space is the weight of a T-invariant curve, as well as a smoothness criterion.
The results rely on equivariant K-theory, as well as the study of different
notions of decomposability of roots.
