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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. 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Varchenko, R. Rimanyi","submitted_at":"2015-09-30T19:50:03Z","abstract_excerpt":"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. 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