Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians

Generalized affine Grassmannian slices provide geometric realizations for weight spaces of representations semisimple Lie algebras. They are also Coulomb branches, symplectic dual to Nakajima quiver varieties. In this paper, we prove that neighboring generalized related by Hamiltonian reduction the action additive group. We a weaker version same result their quantizations, algebras known as truncated shifted Yangians.