  The affine Grassmannian associated to a reductive group $\mathbf{G}$ is an
affine analogue of the usual flag varieties. It is a rich source of Poisson
varieties and their symplectic resolutions. These spaces are examples of
conical symplectic resolutions dual to the Nakajima quiver varieties. We study
the cohomological stable envelopes of D. Maulik and A. Okounkov
[arXiv:1211.1287] in this family. We construct an explicit recursive relation
for the stable envelopes in the $\mathbf{G} = \mathbf{PSL}_2$ case and compute
the first-order correction in the general case. This allows us to write an
exact formula for multiplication by a divisor.
