Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions

Understand

We consider the conormal bundle of a Schubert variety $S_I$ in the cotangent bundle $T^* Gr$ of the Grassmannian $Gr$ of $k$-planes in $C^n$.

• This conormal bundle has a fundamental class ${\kappa_I}$ in the equivariant cohomology $H^*_{T}(T^* Gr)$.
• Here $T=(C^*)^n\times C^*$.
• The torus $(C^*)^n$ acts on $T^* Gr$ in the standard way and the last factor $C^*$ acts by multiplication on fibers of the bundle.