Consider the natural torus action on a partial flag manifold $Fl$. Let$\Omega_I\subset Fl$ be an open Schubert variety, and let $c^{sm}(\Omega_I)\inH_T^*(Fl)$ be its torus equivariant Chern-Schwartz-MacPherson class. We show aset of interpolation properties that uniquely determine $c^{sm}(\Omega_I)$, aswell as a formula, of `localization type', for $c^{sm}(\Omega_I)$. In fact, weproved similar results for a class $\kappa_I\in H_T^*(Fl)$ --- in the contextof quantum group actions on the equivariant cohomology groups of partial flagvarieties. In this note we show that $c^{SM}(\Omega_I)=\kappa_I$.
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机译：考虑对部分旗形歧管$ F1 $的自然圆环作用。假设$ \ Omega_I \ subset Fl $为开放的舒伯特品种，而$ c ^ {sm}（\ Omega_I）\ inH_T ^ *（Fl）$为圆环等变的Chern-Schwartz-MacPherson类。我们展示了一组插值属性，它们可以唯一地确定$ c ^ {sm}（\ Omega_I）$以及$ c ^ {sm}（\ Omega_I）$的“本地化类型”公式。实际上，我们在H_T ^ *（F1）$中的类\\ kappa_I \-上证明了对部分旗标变量的等变同调群的量子群作用的相似结果。在此注释中，我们显示$ c ^ {SM}（\ Omega_I）= \ kappa_I $。
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