Appears in collection : Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday

I will report on joint work with R. Rimanyi and A. Varchenko. We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on weight functions and shuffle products. We obtain an action of the dynamical elliptic quantum groups by difference operators on certain modules over the equivariant elliptic cohomology