Positivity of equivariant schubert classes through moment map degeneration

For a flag manifold M = G/B with the canonical torus action, the T-equivariant cohomology is generated by equivariant Schubert classes, with one class τ_u for every element u of the Weyl group W, and these classes are determined by their restrictions to the fixed point set M^T ~ W. The main result of this article is a positive formula for computing τ_u(v) in types A, B, and C. We identify G/B with a generic coadjoint orbit and use a result of Goldin and Tolman to compute τ_u(v) in terms of the induced moment map. Our positive formula, given as a sum indexed by certain saturated chains, follows from a systematic degeneration of the moment map. In type A our formula is equivalent to a classical positive formula that uses summation over certain subwords, but in type C, the two formulas are different.