Description
Given a representation V of a reductive group G, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This
variety comes with a natural deformation quantization, called a Coulomb branch algebra. Important cases of these Coulomb branches are (generalized) affine Grassmannian slices, and their quantizations are truncated shifted Yangians. Motivated by the geometric Satake correspondence, we define a categorical g-action on modules for these truncated shifted Yangians. Our main tool is the study of how the Coulomb branch algebra changes when we pass from G, V to L, U, where L is a Levi in G and U is the invariants for a coweight whose centralizer is L. I will discuss the relation of our work to the geometric Satake conjecture of Braverman-Finkelberg-Nakajima.
