  Consider the natural torus action on a partial flag manifold $Fl$. Let
$\Omega_I\subset Fl$ be an open Schubert variety, and let $c^{sm}(\Omega_I)\in
H_T^*(Fl)$ be its torus equivariant Chern-Schwartz-MacPherson class. We show a
set of interpolation properties that uniquely determine $c^{sm}(\Omega_I)$, as
well as a formula, of `localization type', for $c^{sm}(\Omega_I)$. In fact, we
proved similar results for a class $\kappa_I\in H_T^*(Fl)$ --- in the context
of quantum group actions on the equivariant cohomology groups of partial flag
varieties. In this note we show that $c^{SM}(\Omega_I)=\kappa_I$.
