  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. We express this fundamental class as a sum $Y_I$ of the
Yangian $Y(gl_2)$ weight functions $(W_J)_J$. We describe a relation of $Y_I$
with the double Schur polynomial $[S_I]$.
  A modified version of the $\kappa_I$ classes, named $\kappa'_I$, satisfy an
orthogonality relation with respect to an inner product induced by integration
on the non-compact manifold $T^* Gr$. This orthogonality is analogous to the
well known orthogonality satisfied by the classes of Schubert varieties with
respect to integration on $Gr$.
  The classes $(\kappa'_I)_I$ form a basis in the suitably localized
equivariant cohomology $H^*_{T}(T^* Gr)$. This basis depends on the choice of
the coordinate flag in $C^n$. We show that the bases corresponding to different
coordinate flags are related by the Yangian R-matrix.
