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For a flag manifold $M=G/B$ with the canonical torus action, the$T-$equivariant cohomology is generated by equivariant Schubert classes, withone class $\tau_u$ for every element $u$ of the Weyl group $W$. These classesare determined by their restrictions to the fixed point set $M^T \simeq W$, andthe restrictions are polynomials with nonnegative integer coefficients in thesimple roots.  The main result of this article is a positive formula for computing$\tau_u(v)$ in types A, B, and C. To obtain this formula we identify $G/B$ witha generic co-adjoint orbit and use a result of Goldin and Tolman to compute$\tau_u(v)$ in terms of the induced moment map. Our formula, given as a sum ofcontributions of certain maximal ascending chains from $u$ to $v$, follows froma systematic degeneration of the moment map, corresponding to degenerating theco-adjoint orbit. In type A we prove that our formula is manifestly equivalentto the formula announced by Billey in \cite{Bi}, but in type C, the twoformulas are not equivalent.

Positivity of Equivariant Schubert Classes Through Moment Map Degeneration